Definitely not a T1, but you're right! it's a traditional looking aimpoint.. but maybe someone can identify it? and the diameter of the battery compartment is way too small for a 2032. I do not know about lr44, since I never had any. how many do I need?
I had that one on my G&P and it is definitely two LR44 batteries. Get the ebay ones as it's under £4 for 12 batteries whereas in the shops it's just under £4 for 2!!!! That way you will always have spares too.