user-1: I have practised previously with the breath, but I feel my eyes fall automatically when setting attention on the breath, and inversely, focusing on objects makes my mind alert. Is this sufficient to switch meditation object? 
Q1: What are the best ways, or the best way, to determine proper meditation objects?
Q2 : Is there any real drawbacks of meditation with a physical object or mental image as compared to the breath?

user8157: The Pali suttas teach to stay with the breath (MN 118). However, it is not necessary to look directly at the breath. Observing the empty mind uses the mind as the meditation object yet awareness of breathing will still occur. 

user-1: Noticing, observing and watching are greatly facilitated by an alert mind. If eyes fall then notice this as bodily phenomena. When you notice the falling of the eyes, what thoughts accompany that action? Watch carefully. You may find that mind is making something out of nothing or that it’s wanting something. An alert mind is sufficient; remaining alert for the duration of the session is quite another thing. Moreover, eyes will move. Let them so.

Q1: What are the best ways, or the best way, to determine proper meditation objects?

There is your attention... and there is your meditation object. If anything comes between the two then attention has been removed from the object. This might include thoughts about bodily phenomena. In fact, thoughts are the number one culprit for derailing ones attention from the object. You can observe bodily phenomena without thought.

Q2 : Is there any real drawbacks of meditation with a physical object or mental image as compared to the breath?

This is personal preference which can be understood further by experimentation.
As further reading I’d strongly suggest that you familiarise yourself with the five hindrances.
The Five Hindrances

user43: Traditionally, meditation object is picked to be an antidote for the biggest remaining emotional problem.
For example:

The person whose mind is dominated by desire, should meditate on ugly aspects of the desired,
For someone whose mind is dominated by aversion, should meditate on lovable qualities of the object of aversion,
Someone whose mind is dominated by conflict between "right" and "wrong", should meditate on Emptiness,
Someone whose mind is dominated by inner chatter, should meditate on the inhalations and exhalations.
Someone whose mind is dominated by doubts, should meditate on basic concepts of dharma: four noble truths, four right efforts etc.
Someone whose mind is dominated by negative self-esteem, should meditate on one's good qualities.

And so on - I think it's easy enough to see the pattern.
I don't think your problem is lack of concentration. All modern people who can read and have finished the high school have enough concentration to be able to skip the kasina stage (meditation on physical objects) and get straight to meditation on mental objects. If I can venture to guess, it sounds like your meditation is too contrived. You are trying to do something synthetic, with no connection to your actual situation. Instead try to look directly at your real-life problems, stay with them enough to face and admit the facts,  then try to come up with an antidote for the emotional disbalance.

-1: <p>I have practised previously with the breath, but I feel my eyes fall automatically when setting attention on the breath, and inversely, focusing on objects makes my mind alert. Is this sufficient to switch meditation object? </p>

<p><strong>Q1: What are the best ways, or the best way, to determine proper meditation objects?</strong></p>

<p><strong>Q2 : Is there any real drawbacks of meditation with a physical object or mental image as compared to the breath?</strong></p>
 8157: <p>The Pali suttas teach to stay with the breath (MN 118). However, it is not necessary to look directly at the breath. Observing the empty mind uses the mind as the meditation object yet awareness of breathing will still occur. </p>
 -1: <p>Noticing, observing and watching are greatly facilitated by an alert mind. If eyes fall then notice this as bodily phenomena. When you notice the falling of the eyes, what thoughts accompany that action? Watch carefully. You may find that mind is making something out of nothing or that it’s wanting something. An alert mind is sufficient; remaining alert for the duration of the session is quite another thing. Moreover, eyes will move. Let them so.</p>

<blockquote>
  <p>Q1: What are the best ways, or the best way, to determine proper meditation objects?</p>
</blockquote>

<p>There is your attention... and there is your meditation object. If anything comes between the two then attention has been removed from the object. This might include thoughts about bodily phenomena. In fact, thoughts are the number one culprit for derailing ones attention from the object. You can observe bodily phenomena without thought.</p>

<blockquote>
  <p>Q2 : Is there any real drawbacks of meditation with a physical object or mental image as compared to the breath?</p>
</blockquote>

<p>This is personal preference which can be understood further by experimentation.</p>

<p>As further reading I’d strongly suggest that you familiarise yourself with the five hindrances.</p>

<p><a href="https://www.accesstoinsight.org/lib/authors/nyanaponika/wheel026.html" rel="nofollow noreferrer">The Five Hindrances</a></p>
 43: <p>Traditionally, meditation object is picked to be an antidote for the biggest remaining emotional problem.</p>

<p>For example:</p>

<ul>
<li>The person whose mind is dominated by desire, should meditate on ugly aspects of the desired,</li>
<li>For someone whose mind is dominated by aversion, should meditate on lovable qualities of the object of aversion,</li>
<li>Someone whose mind is dominated by conflict between "right" and "wrong", should meditate on Emptiness,</li>
<li>Someone whose mind is dominated by inner chatter, should meditate on the inhalations and exhalations.</li>
<li>Someone whose mind is dominated by doubts, should meditate on basic concepts of dharma: four noble truths, four right efforts etc.</li>
<li>Someone whose mind is dominated by negative self-esteem, should meditate on one's good qualities.</li>
</ul>

<p>And so on - I think it's easy enough to see the pattern.</p>

<p>I don't think your problem is lack of concentration. All modern people who can read and have finished the high school have enough concentration to be able to skip the kasina stage (meditation on physical objects) and get straight to meditation on mental objects. If I can venture to guess, it sounds like your meditation is too contrived. You are trying to do something synthetic, with no connection to your actual situation. Instead try to look directly at your real-life problems, stay with them enough to face and admit the facts,  then try to come up with an antidote for the emotional disbalance.</p>
