Hi Steve,
I checked with the stuff I took out of my tug earlier (replacing it with standard RC-material, like so many conversions on this forum) and you're correct in your assumptions;
The single black wire should be soldered to the terminal where at present only the capacitor is connected to (capacitor = brown thingy), the red wire is connected to the other terminal, also together with a capacitor.
The other pair should be soldered onto the motor for the squirter.
The motor has to be connected the right way around, otherwise the pump won't work.
If I remember correctly the motor should run counterclockwise, seen from the connector side, but that's a matter of trial and error, as mine has blue and green wires...
Regards, Jan.