Q:

At what point do you count as interacting with an illusion?

When you are in the presence of an illusion, at what point do you count as having interacted with it, granting you a will save to disbelieve?

A:

Whenever you spend at least a move action to interact with it
This interaction is explained in detail on the Ultimate Intrigue sourcebook on a chapter called Spells of Intrigue, the book discusses a lot of the inner details on how several schools of magics should be handled on adventures that have some kind of intrigue, like politics or social interaction between PCs and NPCs, including conjurations, enchantments, necromancy, divination and illusions. On the topic of Illusions (page 158) we have the following:

Disbelief and Interaction: All three of the subschools
  above tend to have saving throw lines that say “Will
  disbelief,” but they differ in how those saving throws apply.
  Phantasms directly assail a creature’s mind, so the
  creature automatically and immediately receives a saving
  throw to disbelieve a phantasm. Figments and glamers,
  however, have the more difficult-to-adjudicate rule that
  creatures receive a saving throw to disbelieve only if they
  “interact” with the illusion.
But what does it mean to interact with an illusion? It
  can’t just mean looking at the illusion, as otherwise there
  would be no need to make the distinction, but drawing
  the line can be a bit tricky. Fortunately, the rules can
  help to define that difference. A creature that spends a
  move action to carefully study an illusion receives a Will
  saving throw to disbelieve that illusion, so that is a good
  benchmark from which to work.
Using that as a basis, interacting generally means
  spending a move action, standard action, or greater on a
  character’s part. For example, if there were a major image
  of an ogre, a character who tried to attack the ogre would
  receive a saving throw to disbelieve, as would a character
  who spent 1 minute attempting a Diplomacy check on
  the ogre. A character who just traded witty banter with
  the ogre as a free action would not, nor would a character
  who simply cast spells on herself or her allies and never
  directly confronted the illusory ogre. For a glamer,
  interacting generally works the same as for a figment,
  except that the interaction must be limited to something
  the glamer affects. For instance, grabbing a creature’s ear
  would be an interaction for a human using disguise self
  to appear as an elf, but not for someone using a glamer
  to change his hair color. Similarly, visually studying
  someone would not grant a save against a glamer that
  purely changed her voice.

The Pathfinder SRD, which is not an official source of info, lists these rules on the same page as other optional rules systems, probably due to how recent they are and the lack of a proper categorization from paizo (Ultimate Intrigue is not yet listed on the official PRD), and thus, that might lead readers to think that those rules are unofficial or not part of the rules as written. But that's not the case, the book does not mention that those rules are to be used together with the intrigue system (from the same book) or label those as optional anywhere. The text actually talks about those as clarifications or guidelines to help GMs decide how to use those type of spells (illusions, enchantments, divinations, etc) on their campaigns, similar to the guidelines found on the Gamemastery Guide. You will notice that those rules are not actually making up new rules, but working on what is already written in the core rulebook and expanding it.
Discussing what is offcial or not is not the objective of this answer, but this clarification was needed based on feedback from comments. Should be enough to say that several systems are labelled as optional on the books, but have been used on official published adventures, like modules, adventure paths and pathfinder society adventures. Including material from this book, like the research library rules used on Mummy Mask Adventure Path.
That said, since the Ultimate Intrigue is a fairly recent source book, you should consult with your GM if it is allowed as rules or not. Otherwise, the term interaction is vague and will suffer table variation.

