Patur Aval Assur,
In your quotation below, the text in bold are my clarifications based on how I understand you.
In short, the criteria are that it has to be something that has a non-benefit related reason to follow it but doesn’t have a benefit related reason to follow it.
So to shorten your question, you are asking us to provide a reason for doing anything that is unrelated to benefit.
The best answer I can come up with is this:
We humans are ephemeral and limited, therefore it is possible for us to receive benefit that makes us longer lasting and stronger. It makes sense, therefore, for human beings to act for their benefit, and we call this sense “reasons” for acting.
Since G-d is eternal and omnipotent, it is nonsensical to state that He can receive benefit. Yet, we know that He does things, so He must have reasons that are unrelated to benefit. We are incapable of knowing these reasons due to our own limitations.
So why would a human being do something if not for benefit? It doesn’t really make sense to us, and your conundrum would stand, except for one thing: human beings were created b’tzelem Elokim. Therefore, there is a spark from Hashem inside each one of us. So even though we cannot articulate it with the earthly definition of “reasons” that you seek, if all “benefit” reasons for an act are stripped away, we are still left with the reason that Hashem does things. What is that reason? Ask Hashem. But it’s within us, whether we can articulate it or not.