If you're powering the lights with 5V or 9V, just use copper tape (used as a snail barrier in gardens) for the V+ and ground and apply them to the lets or to the center column (as long as they're isolated from each other).
The copper strip doesn't have to be very thick - 1/16" - 1/8" should do the trick. Just solder the connections before applying the tape to the plastic! The stuff I bought is sticky on one side, and can be primered/painted. You would use a metal contact in the base to connect the ship to its power supply. If you do a leg and the central column, there's no chance of inverting the polarity. And we know what happens when you invert the polarity on most spaceships!