I recently purchased a full size replica bronze Corinthian helmet from Greece. In some Greek pottery images and sculptures notably the one of Pericles of Athens, the helmet is placed in the "rest position". Now I've tried this with the bronze replica that I have and when I place it in the "rest position" it is top heavy and easily able to fall off my head when I moved my head rather slowly from side to side. it is also uncomfortable since the bottom half of the helmet is placed on my neck, I'm practically balancing the thing on my head.
So the conclusion that I've drawn from this , is that I can see it being in sculptures and pottery images since it does look aesthetically pleasing but I can't see it being actually used as a "rest position" since it would make more sense just to take the helmet off.
Maybe on the smaller helmets I could see it being used this way...?
see images below
The helmet raised to rest on top of the head seems to be just an artistic convention. In the specific case of Perikles it was also to avoid drawing attention to the unusual shape of his head. I wrote about this in an older thread. To my knowledge there is no literary reference to pulling the helmet down for battle. It's a good example of why we should be hesitant to rely on art as a guide to ancient weapons and their use...