As Jerry said, they're just a solenoid that get's energized with power.. Off and the valve pulls from the default tank. Powered or energizes the solenoid moves blocking the default port and opening the aux tank port.
Normally when they don't work it's because the solenoid seized. I do know a guy, and I watched him do it to his 77 C20, he took the valve off and cleaned it up. He had an extension cord with the end cut off it. With nothing to lose he said we was going to Zap it and see what happens. He clamped 1 wire of the extension cord to the body of the valve, plugged it into the wall at 110V, then dragged the other wire across the positive lead to the valve. I mean, just wiped at it quickly and that was that. We heard something and figured it was the valve toasting. Nope, it was the solenoid moving. Right after he did this zap with 110V, he put it on the barrery and hooked it up. Solenoid moved, disconnected, solenoid moved, squirted a little trans fluid in both intake ports and repeated a few times hooked to the battry, connect - disconnect - connect - disconnect. We could hear the solenoid moving freely. He reinstalled and problem was solved. Both tanks worked again for as long as he kept the truck.