As
@1poolman1 says, it’s probably a version of the 10” Amerlite. It’s similar to many I’ve seen, not exactly like mine so I’m not certain. When you remove the gasket from the lens you may find a part number etched into the outer rim of the glass and/or on the gasket itself if that’s possibly readable.
More suggestions that you’ll see also among many other related TFP threads… Definitely replace the gasket with a new one, most instructions demand that every time you open the luminaire housing. Clean all gasket contact surfaces to perfection, and I prefer coating them also with a
non-petroleum based lubricant like Jacks Magic Lube as other lubricants will deteriorate the gasket. Note also most replacement gaskets are stamped “this side facing pool”. A new stainless steel pilot screw is in order as well – will save you down the road.
I feel compelled to note that many or most locales also demand an electrician for much of this. It’s possible your transformer is okay, two reasons. You may have the meter on “DC” – the transformer outputs 12VAC (or 13 or 14 depending on primary tap used). It’s also possible a downstream wiring short would cause the zero reading. The only way to be certain is to disconnect the load side at the transformer and measure for 12vac from the transformer secondary. In the case of a short, some transformers will cut out due to overload and reset themselves after they cool off.
Given the age, a replacement luminaire may also be smart. It would also be wise to replace the circuit breaker with a GFCI breaker. There is some controversy about that but it’s still wise and safer, given the possible ways of screwing up the transformer wiring, especially in older installations – hint about electrician again.
There are so many bulbs to choose from it’s dizzying. For $61 there are ones
like this bright white one, or RGB colors like this
other color one for $40. But…. Given your possible need for a luminaire housing, transformer and bulb, package solutions are getting popular.
Like this one for $300, and there are many others in that price range. Look for one that has a waterproof control/transformer that can be mounted near where your old one was – requires running new wire all the way through and some come with 50 to 150 foot cords. Electrician makes sense for all those and a GFCI breaker still smart regardless of how safe you might think the new transformer is. Check also that any choice is UL rated and approved for pool use - I don’t see that advertised very often, don’t know what’s up with that. I even noticed some that are 24 volts which I think creates new and interesting electrical code requirements., so personally I’d steer away from 24 volts. Quality, function, brightness and longevity/reliability seem to vary a lot among bulbs and full package solutions, hard to say. Perhaps someone has a recommendation or maybe found in other TFP threads if you dig around. Online reviews may help if you can trust such things.