yup, sounds like it.
Ok then, the second solenoid is a timing advance (its inside the pump, or on the back/top), its purpose is to advance the injection point only whilst the engine is cold, there is a thermostatic switch that controls it, once the motor has warmed up the thermostat switches off (the opposite to a radiator fan switch) and de-energises the coil, the thermostat is usually in the cooling water stream.
You dont have to wire it up, what'll happen without it is the engine will idle erractically and will have reduced power for the first few minutes, so if your in a rush you could leave it for later.
The device you found with 2 wires out the back sounds like the thermostat, but not definately.
I would chase the wire that dissapears into the head and determine exactly what its wired to.
Also the stop solenoid wire, does it only go to the solenoid, or does it look like it could go somewhere else as well, some advance solenoids share the same + as the stop solenoid, and the - goes through the thermostat to earth (sounds a bit like what you might have).
The general idea is that the ignition supply goes through the thermostat then to the solenoid, or the ignition supply goes direct to the solenoid and the earth goes via the thermostat.
Take the device with 2 wires out the back off, meter it with you tester then dunk it in hot water, if it reads a short when cold and open when hot then it is the thermostat for the cold advance solenoid.
Also a look at the schematic for the donor car would give you some other ideas.
You could just connect a switch on the dash to the advance solenoid and control it manually, I like this idea.