65 - no dash lights

The car is not in front of me now, but if I remember correctly, the instrument lighrts are on the first panel fuse. the second fuse indicates stop/tail lights. That fuse is fine, no heat and is working properly.

Interesting idea about the HL switch. I may be easier to swap it out, than to pull and reattach the round big connector. The connector is right behind the dash support, so to get at it, I'll have to pull the cluster.
You are correct, the instrument panel lights are on their own circuit. Power goes from the light switch to the fuse panel and then on to the circuit board on the back of the cluster. If there is no problem with the wiring from switch to fuse box (not common), the problem is in the circuit board and dash lights. If it has the wrong dash light bulb holder(s), they can short or ground out. The only decent way to check it is to pull the cluster and inspect each light and connections. You can try pulling the bulbs you can get to easily and retesting if you like but if the cluster hasn't been out in a while, it's a good time to lube the speedo, tighten connections, and replace bulbs.