As a GM, how do you decide when a creature has discerned an illusion for what it is?

Many illusion spells, such as minor illusion and silent image have a clause that reads:

If a creature discerns the illusion for what it is, the illusion becomes faint to the creature.

The illusions often have a method or two in the spell description explaining how a creature can determine there’s an illusion, but I’m wondering what other methods, if any, would allow a creature to discern an illusion.

This answer states (and I concur) that there’s nothing in the text that would indicate that the methods given are the only methods to discern the illusion and many people seem to agree that illusionists are not subject to their own illusions, even though that isn’t explicitly mentioned in the spell description; another potential method for discerning illusions is by being told by a trusted ally that the object/creature is an illusion, although I don’t see people talk about that as much. Thus, it seems likely there are more potential methods people may be familiar with as well.

What methods do you allow characters to use to discern illusions outside of those that are mentioned in the spell description, why, and how do you effectively communicate your decision on the issue to players? I suspect there has to be a consideration of game balance, ease of adjudication, and believability, among other things, so I’m hoping to hear about how decisions actually play out when used at the table.