Strangest ceiling fan issue I’ve ever encountered. Fan works, lights do not, everything checks out with the ‘ok multimeter

I have a handful of identical ceiling fans in my home - the one in question doesn’t have a brand logo (emblem is long gone) but I can make out “52-BRW” as the model number. This ceiling fan has one switch that powers it, and the fan and lights are controlled via pull chain.

In one of these specific fans the “fan” portion works fine, but there is no light. The pull chain does nothing. The “light kit” is connected with two wires, which show ~120v across them when them, and I show 120v in the sockets themselves when everything is plugged in and turned on. The problem is, even showing full voltage, there is zero light. What I’ve tried/checked:

• Swapped an identical light kit from another fan - the kit from this fan works in a different one, and the known good kit from a different fan does not work in this one. In my mind this rules out the light kit itself.

• Checked continuity from the wires running to the light kit to the bundles/caps where they all come together - all good

• Tried old school incandescent bulbs - still nothing (just to rule out LED weirdness).

This fan was pre-existing when I bought the home so I have no idea if this is a new issue or something that’s been broken for years. My next step, in my mind, is to take the whole unit down and check basically every possible connection for continuity. I really want to avoid replacing the fan since I can’t find another and I’d have to replace multiple fans to make them match.

Any ideas? This one really has me stumped…