Finally got over to look at the mast (not stored at the marina). The VHF coax has no connector, and will need one, but there is a large gauge "lamp cord" for the lights. From what I can see it is 12 gauge. Rubber insulation seems to be in good shape (flexible and not dried out) but only 2 conductors. Either the anchor light and steaming light both go on and off together, or they use the mast for ground, but didn't see a terminal on the mast itself to connect the mast to system ground. It's also possible this is someone's 'repair', and only 1 light is actually wired.
Didn't have any tools, or flashlight (unplanned trip, I was on that side of the river and just stopped to look) so I couldn't see inside the mast to see if there is a conduit.
The anchor light needs to be replaced, socket and connectors badly corroded. Didn't open the streaming light to inspect inside, though the outside looked much better than the masthead light.
Next time I will bring a couple tools, and someone to see if existing wire is anchored or can be used to pull a pull string. I never use old wire to pull new. A string offers less resistance, is more accommodating, and is less likely to break when pulling in the new wire.
Looks like new LEDs are in order, at least for the anchor light, probably both.