I must say a huge thank you to everyone who responded. I was really feeling like nothing I was seeing made any sense at all and I started to see that not only was there sense in what I was seeing, there were also a lot of clues. I must admit I was also really grateful to have my trusty factory 1971 Pontiac shop manual which has a truly amazing fold-out electrical diagram.
Here's what I did. I made some jumper wires for testing. I first tested that the lights worked if I jumped to the wires at the high/lo footswitch. They did
After verifying all that worked both on its own and with the relays I was able to put the lights back in and work on where the fault was upstream of the light switch. I realised that the big distinction between the headlights (which didn't work) and the side lights and all (which did) was that those other lights are fused and the headlights aren't. That meant they had two different feeds.
I realised that since a bunch of the other stuff that was working was fed from the same splice I had better dig in and unwrap all the factory wiring bundle so I could see the state of the connections and fusable links and such. It was then that I narrowed my search down to a red wire that powers the headlight switch bypassing the fuse box. Protecting it is a green fusible link. I got the bundle open and I could clearly see where the fusible link was burnt out because I could feel a small section where the wire seemed to be missing. I cut the insulation here and decided the best way to deal with it would be to just join it back together here since the rest of the wire was intact.
The exercise was worth doing because I was able to find and correct some other connections that were less than perfect.
Of course, nothing could be that easy and I found that although I had lights the instrument panel lights were now not lighting. This turns out to be governed by a stupid fuse that is half the length of any normal fuse. Any idea where you get one of those? But apart from that everything is now working again!
Sam