Sounds to me like the solenoid has failed and is shorting to earth internally. I mean, it must be connected to earth for it to recognise the issue. Will have most likely blown a fuse also as without a resistive load, far too much current will have flown through the circuit. I have problems at work with central heating/hot water solenoids shorting out internally quite often. I'd look into getting it replaced.
I doubt the reversing lights are related, probably a conicidental, separate issue. Not sure what though