1964 Valiant HEI troubles

I recall that my 65 had 3 wires to the ballast, but it is a V-8 and yours had a slant (throttle rod, not cable). Check the wiring diagram. Regardless, you should connect all the wires together that went to the ballast.

12.25 V should be fine. You could trace down the voltage drops from BATT+ to your relay and after, if you truly care. I assume the engine is not running, otherwise you should see ~14 V w/ the alternator turning.

Is you HEI module on the backside of the plate? Is that black wire hanging the ground for the HEI case? It won't work unless you ground it well (no drop to BATT-). You have exposed copper on the 12 V feed spade terminals, so cover that before you drive the car.