Do you have spot lights. Wired into the headlights which are activated when high beam is selected. if after market and wired incorrectly although through a relay could be an issue there. I have seen strange wiring in the past where aux lights were wired incorrectly and caused all sorts of issues if a fuse or relay has failed. Do the side lights illuminate and stay illuminated when the engine is running and not running?
I'm fairly sure the silver tops had a rudimentary alternator which had the charge control attached ie self regulating. Have you checked all other electrical functions, perhaps when you put the multi-meter across the battery., Battery with no load should should read close to 12.6v and with engine running in the region of 14.2or3v. Whilst observing the running charge you could initiate a load IE turn the heater on to full blow and the alternator should accommodate this very quickly.
What happens when you flash the high beam with the engine running and headlights switched off?
Gaufridus, I'm sure you are not the first person who has encountered this. If I look at it from this distance my first thought is that, headlights come on with ignition on yet when alternator charges after starting they go out..... I'd be looking for a relay fault and or wiring that is isolated by some failure of a component or a short but, if Richard hasn't come up with an instant solution then it might be a bit of a methodical slow assessment!
