In reply to alx:
In hindsight I should have really reread your OP!
So at best when your climbing well you have an awareness of what different parts of your body (proprioception) are doing without having to put conscious effort into doing it. You seem to take a back seat in the whole thing and you think your way through the process. But when thinking, your not consciously thinking left arm, right arm etc, it's more like I need my right hand there and it happens.
I would google, gold medal bodies and check out their fundamental basics videos. Bear crawl, frog, gecko and movement patterns you can do on the floor and crawl back and forth, they use similar pattern movements but horizontal rather in the vertical.
Good luck!