user-1: "Not doing" in this sense is to mean the absence of any form of action that originates from thought (for instance physical form like speech, bodily movements) in such a way that reduces the physical forms impact upon sentient beings in its environment.
I realise that I'm heading into one of the unconjecturables here but for practical purposes. I don't think it'll lead me to vexation. This curiosity has arisen through partial insight into karmic laws in which the knowledge of karma became demystified into a rather obvious, almost mechanistic natural working of things. I wanted to try to understand at least from the periphery of the insight, from what Buddha said and from what others practising Buddhism understand so that I can cross-reference the three.
Additional
In an example from the Buddha, he chose not to be a father to his son, Rahula (not doing) in favour of seeking his own liberation. His thoughts were of himself. I imagine this would have caused considerable discomfort in Rahula and this discomfort would have been further compounded when Rahula learned of the meaning to his name: fetter or ball and chain.
In an example from my own experience, a person became quite angry with me last week. I remained calm and non-responsive, guarding the senses - essentially watching after myself. I still gave a portion of my attention to the person via eye contact. Because of my "not doing" they became more frustrated. I recall thinking, "this person is lost in their emotions". I received a message from them later that day saying they had cried and let it go.
*As I write this addition, Andrei's answer below seems to resonate here. 

user14060: Generally karma stems from sankharas , but the non bright and non dark karma cannot stem from a sankhara since it ends the rebirths.
this ad hoc karma called non bright and non dark stems from right view and right resolution, which follow from  the discrimination between thoughts of renunciation and good will and other thoughts, and embracing only thoughts of renunciation and good will. Whatever actions following those thoughts will be ''tainted'' by the only karma that leads to the ''ending of karma and rebirth''.
In terms of actions, this weird karma colors the right talks, right actions and so on, with their pinnacle being right samadhi. SO there are plenty of actions stemming from right view, but most of those actions have nothing to do with most of the actions invented and done by puthujjanas.

user111: 
Cetanāhaṃ, bhikkhave, kammaṃ vadāmi. Cetayitvā kammaṃ karoti: kāyena,
  vācāya, manasā.

"Intention, I tell you, is kamma. Intending, one does kamma by way of body, speech, & intellect."  - Nibbedhika Sutta
So as you can see, Karma is the intention. These intentions may or may not be followed by verbal and bodily actions in which case they are categorized as verbal karma and bodily karma. When there are no bodily or verbal actions involved they are called mental(mano) karma. But it is Karma nonetheless. There is no Karma without the mind.
For an unenlightened person, there is no experience without Karma. Every experience has a maximum of 17 thought moments. Seven of these thought moments are called the Javanas. They are Karmically charged.

user43: Rephrasing Buddha, there's action that leads to good experience, action that leads to bad experience, and action that leads to dispassion and liberation.
Of course the word "karma" itself means "doing" or "action". But my teacher said, the wise sees nondoing in doing and doing in nondoing. Meaning, if you choose to drink coffee, you implicitly choose to not drink tea on that occasion and vice versa. In Mahayana terms, an "act" is empty. It is something we isolate and put a label on but in actuality it is just a point we focus on in context of everything else. When we begin seeing it like this, we begin getting closer to the Buddha's perspective.
As my Zen Master said, whenever there's choice, there's confusion. From Buddha's omniscient perspective, there's no more confusion, no action, no choice - only from the perspective of a sentient being.
Another thing that needs to be said, not all karma is personal, which makes sense if you realize that "person" is another empty point of focus. There's also group karma and other even broader kinds of karmic tendencies that don't rely on an individual action per-se. So even if you don't personally act (don't choose) you are still subject to these extrinsic tendencies. It's only when you are free from any group identification as well, is when you begin to get free from the fruits of karma.
Sorry, upon rereading this I can see it comes out a bit unclear, but this is a summary of my understanding as of the moment, based on what I have learned. 

-1: <p>"Not doing" in this sense is to mean the absence of any form of action that originates from thought (for instance physical form like speech, bodily movements) in such a way that reduces the physical forms impact upon sentient beings in its environment.</p>

<p>I realise that I'm heading into one of the <a href="https://www.accesstoinsight.org/tipitaka/an/an04/an04.077.than.html" rel="nofollow noreferrer">unconjecturables</a> here but for practical purposes. I don't think it'll lead me to vexation. This curiosity has arisen through partial insight into karmic laws in which the knowledge of karma became demystified into a rather obvious, almost mechanistic natural working of things. I wanted to try to understand at least from the periphery of the insight, from what Buddha said and from what others practising Buddhism understand so that I can cross-reference the three.</p>

<p><strong>Additional</strong></p>

<p>In an example from the Buddha, he chose not to be a father to his son, Rahula (not doing) in favour of seeking his own liberation. His thoughts were of himself. I imagine this would have caused considerable discomfort in Rahula and this discomfort would have been further compounded when Rahula learned of the meaning to his name: fetter or ball and chain.</p>

<p>In an example from my own experience, a person became quite angry with me last week. I remained calm and non-responsive, guarding the senses - essentially watching after myself. I still gave a portion of my attention to the person via eye contact. Because of my "not doing" they became more frustrated. I recall thinking, "this person is lost in their emotions". I received a message from them later that day saying they had cried and let it go.</p>

<p>*As I write this addition, Andrei's answer below seems to resonate here. </p>
 14060: <p>Generally karma stems from sankharas , but the non bright and non dark karma cannot stem from a sankhara since it ends the rebirths.
this ad hoc karma called non bright and non dark stems from right view and right resolution, which follow from  the discrimination between thoughts of renunciation and good will and other thoughts, and embracing only thoughts of renunciation and good will. Whatever actions following those thoughts will be ''tainted'' by the only karma that leads to the ''ending of karma and rebirth''.</p>

<p>In terms of actions, this weird karma colors the right talks, right actions and so on, with their pinnacle being right samadhi. SO there are plenty of actions stemming from right view, but most of those actions have nothing to do with most of the actions invented and done by puthujjanas.</p>
 111: <blockquote>
  <p>Cetanāhaṃ, bhikkhave, kammaṃ vadāmi. Cetayitvā kammaṃ karoti: kāyena,
  vācāya, manasā.</p>
</blockquote>

<p>"<strong>Intention, I tell you, is kamma</strong>. Intending, one does kamma by way of body, speech, <strong>&amp; intellect</strong>."  - <a href="http://www.buddha-vacana.org/sutta/anguttara/06/an06-063.html" rel="nofollow noreferrer">Nibbedhika Sutta</a></p>

<p>So as you can see, Karma is the intention. These intentions may or may not be followed by verbal and bodily actions in which case they are categorized as verbal karma and bodily karma. When there are no bodily or verbal actions involved they are called mental(mano) karma. But it is Karma nonetheless. There is no Karma without the mind.</p>

<p>For an unenlightened person, there is no experience without Karma. Every experience has a maximum of <a href="https://www.accesstoinsight.org/lib/authors/mendis/wheel322.html#citta" rel="nofollow noreferrer">17 thought moments</a>. Seven of these thought moments are called the Javanas. They are Karmically charged.</p>
 43: <p>Rephrasing Buddha, there's action that leads to good experience, action that leads to bad experience, and action that leads to dispassion and liberation.</p>

<p>Of course the word "karma" itself means "doing" or "action". But my teacher said, the wise sees nondoing in doing and doing in nondoing. Meaning, if you choose to drink coffee, you implicitly choose to not drink tea on that occasion and vice versa. In Mahayana terms, an "act" is empty. It is something we isolate and put a label on but in actuality it is just a point we focus on in context of everything else. When we begin seeing it like this, we begin getting closer to the Buddha's perspective.</p>

<p>As my Zen Master said, whenever there's choice, there's confusion. From Buddha's omniscient perspective, there's no more confusion, no action, no choice - only from the perspective of a sentient being.</p>

<p>Another thing that needs to be said, not all karma is personal, which makes sense if you realize that "person" is another empty point of focus. There's also group karma and other even broader kinds of karmic tendencies that don't rely on an individual action per-se. So even if you don't personally act (don't choose) you are still subject to these extrinsic tendencies. It's only when you are free from any group identification as well, is when you begin to get free from the fruits of karma.</p>

<p>Sorry, upon rereading this I can see it comes out a bit unclear, but this is a summary of my understanding as of the moment, based on what I have learned. </p>
