In future, please only post questions once, if its not in the right place, we can move it to where its best suited.
Ok, the problem. This is an easy test actually. You have three wires, white, black and red. Black is ground, the other two are pull and hold, i'n not 100% sure on this, but i think white is pull, red is hold. To test, ground the black wire, touck the red wire to the +ve terminal, if it does not snap back try the white. If you hear it snap and pull the lever back, this will tell you which wire is for the pull coil and the other is the hold.
Now, if you put power in the hold coul and touch the pull coil wire to the +ve terminal, touch it then let it go, the solenoid should be holding the lever in place, when you let go of the hold wire, it should snap back to the off position.
Does any of that make sense?
Just never hold the pull wire on the battery though, this coil is designed to be powered for only a few seconds, too long and it will burn out, the hold coil is designed to run all day.