Yep that's pretty much what I meant about "finding" the trigger- the grey lead would go there once everything's figured out.

I guess the next step would be to confirm the black and red leads when touched together cause the high beams to illuminate. Just try touching them together and see if that works. If so, then you know you've got all the right wires, and they're all performing as we expect them to.

The dome light circuit may also power the 12 volt trigger that is supplied by the turn signal stalk when you engage the high beam signal function.

I would start here by hooking the grey trigger lead to the relay where we think it goes, then pull on the stalk and make sure the relay makes a click. If not, then either the relay's faulty or it's the wrong type.

Hope that helps.
Dylan