break light electrical

Not a bad connection in the steering wheel but below it in the signal switch.
Brake lamp power should go up the column on a white wire and come back out toward the rear lights on yellow and green. Only when the signal switch is in its centered position though. When that switch is moved to left or right turn positions the coreponding green or yellow wire gets its power from the signal circuit.

Yes the coil should get 7 to 8 volts in run and 12 volts only when switch is in start position.