Pool Light Keeps Burning Out
My first comment is old lamps if correct may have leaked and allowed atmosphere in and the filament burned up, lamps over 300w are quite rare and most have been replaced by HID over the last 40 years.
More realistic HID ( metal halide or sodium vapor ok with a ballast)   Are you sure you don’t have a ballast in there somewhere?
Open circuit voltage for a sodium s55 could be there but when the starter strikes in a few seconds it’s high voltage pulse would blow a incandescent filament.
I think this may be what is happening if not old stock.
the original lamp could have been a 500w equivalent sodium  at 150 actual watts because hid’s usually are 400w the next size is 1000w that is actual watts but equivalent is Close to 150w so now you know why most changed years back
a 500w lamp will have a mogul base and only produce 10k lumens . A 150w high pressure sodium may have been classed as a 500w equivalent the open voltage would be in the range you measured Or close 110+ I did not discuss metal halide because their open circuit voltage is 2x what you measured and HPS has a much higher strike value.
So we have old stock incandescent mogul base or a possible HID lamp that has a ballast and starter , I can caution you if your meter is not rated do not try and test the strike voltage most meters are only good to 1kv for the test leads up to 5kv but some HPS have strike voltages from 12-20kv , I learned this with a fluke 87 many years ago.
For well under 100$ you can get a LED flood almost any brand will put out 500w equivalent and consume 75w with higher end ones only drawing ~60w
And they will last 50000 hours compared to 2000 of an incandescent.