card should be what turns on the coil driver, coil driver provides connection to negative (wire 13). should be the same in forward and reverse after the driver.
It seems to me to be a strange way for the driver to go bad (but not impossible. got a bac-a larm installed??
I would want to check bypassing the coil module (wire 13 is neg),
what you have sounds like the coil armature (the part that holds the moving tips and is pulled down by the coils magnetic field) has a little guide pin in the bottom and this pin may have come loose or be missing.