Right, so they're either emitter or collector. Base would then be the single wire left over and the counterpart the big terminal bonded directly to the thin film circuit.

Beautiful bit of history, thank you very much for taking the time to do this one.

But matching the schematic to the picture, the double wires are on the base. It makes me think it's a double-base transistor, but both bases tied together because they don't need two for this circuit.

If it was for reliability, I'd expect the emitter to also be doubled, but it has a single wire.

GE made the 3N36/37, but here's a datasheet for a similar part: http://bitsavers.org/components/ti/discrete/transistors/3N34...

That means it is definitely not for current. The current to the base would be negligible compared to the EC current.