With positive meter lead on br/bl pin in relay and negative meter lead on negative battery, 11.8 v goes to 12.3 v when starter button pushed. Pin for black wire stays at 12.3 v.

So the starter switch is bad? It should go to 0 v when starter button pushed? I get the same readings (11.8 to 12.3 v when starter button pushed) at the two connections inside the headlight shell where the br/bl wire connects into and out of the connector block.

I have a replacement switch. If I wanted to test this new switch without completely wiring it in, what are the minimum connections I would have to make to test if the new switch solves the problem? Would I have to connect more than the br/bl wire into the connector block and maybe the grounding brown wire with a spade connection?