To operate the solenoid - it needs to have 12v across it - a differential so that current can flow. If each side is 12V then no current can flow. Similarly if each side were zero volts there would be no current flow.
You would do well to investigate just what it is that makes one of those 12 volts go away at shut-off time.
I know nothing of tractors - just very basic electricity.
Good Luck..., February 2016