Rich -:
When I "just sit" without intention then I seem to go through peacefulness and lack of attachment much more than if I'm looking at anything in particular.
When I look at self, watch the self arising or ask "who am I?" then it actually appears like the self becomes much bigger, stronger, and, paradoxically, more slippery and impossible to see "from the outside".
Is there an aversion being triggered for the experience of something assumed to be 'self'? If so, perhaps become aware of that mental push and pull of aversion towards whatever is perceived. Experiemnt with complete 100% acceptance of that experience you describe (the growing of a sense of 'self') and simply be curioius as to what will happen next WITHOUT ANY EXPECTATION WHATSOEVER.
And/or perhaps if so inclined, explore what that sense of 'self' is actually made up of, a mental overlay? a supporting sensation somewhere in the body? A mental image? Break it down no matter how 'big' it seems to get. Notice any aversion for sch an experience as well and include it in a panoramic viewpoint including both the sense of 'me-ness' and sense of aversion...at the same time and dispassionately watch curious as to what will happen next, WITHOUT ANY EXPECTATION WHATSOEVER!
Curiously the same thing more or less applies with suffering. If I look at pain then it can also sometimes increase, become much less bearable, and cause a lot more suffering.
Attention is bringing more awareness to what is arising, the mind is making whatever it is that is arising into an mental 'object' to then subjectively react towards with aversion...and thus it seems like it has grown in quantity and quality and misery. Same as above, become aware of the sense of mental aversion at the same time as the other phenomena (object of attention). See what happens next etc.
This seems to be the opposite of what should be happening. So what is happening here?
It would seem you have established a big subtle 'should' belief (e.g. it should be that way not this way) within the mind which now conditions how experience is experienced, either with aversion or craving. Question that 'belief' and allow it to be seen as just a locked in thought loop conditioning how you practice (i.e.not wanting experience to eb a certain way, wanting it to be as it 'should'). Becoming aware of it and allowing it to be seen as it arises and ceases will show its cessation more often than not.
I always understood that equanimity meant that it doesn't matter if there's self or pain or whatever, you're just tranquil either way. So how do you encourage that to arise if the very act of being with pain or self causes them to appear bigger and less bearable?
Question and explore, discern and cultivate dispassion for the sensations of aversion for such experiences and the craving for something 'should', otherwise you will be eternally disappointed.
Nick