Using a DVM can some times give false readings due to its high impedance (very very little current flows through it)
so a "dirty" switch contacts have just enough continuty to SHOW 12Vs, but when a resistance load aplied, not enough current go through to run the motor.
when you saw the random numbers, that was an indication you were measuring a piece of wire that should be seperated from 12V and ground, but just enough "dirty" to cause volt readings.
Thus I think using a light bulb to replace the motor would let you KNOW when power is being applied. Now, a single bulb will not tell which way the motor would spin, however, with a couple diodes you could make a dual bulb indicator.
using a bulb and the hand crank seems like the safe way to set those limit switches