I know Matt's car a bit, he's had it for maybe 30 years.
It was converted from AT to the Tremec several years back and has been driven a fair amount since.
But IIRC it does sit for periods of time in his home garage.
That tells me something has changed or deteriorated.
I've had a starter relay with a loose terminal that would occasionally no-start; wiggle the connection, and it would work.
Matt, look at the other end/connection of whatever grounded the relay before, including the wire itself.
Could even be a faulty replacement relay, ground shouldn't be carrying 12V, right ?

Dash lights: so the dimmer rheostat works the A/M gauge lighting OK, but not the cluster lamps ?
I'd look at whatever the different routing for those two is, including the big connector at the back of the cluster circuit board.