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...