If that contact is closed and you only see 20 volts that is a problem, it can be hard to watch as the contact may close and cycle open fast, record button on a good meter will help with that.
Also what was the coil resistance?

Jumping b+ to the lower side of the contact may work. You have to apply the voltage at the same time as the truck is commanding the contact closed. This truck is to smart for its own good.

You can also power the truck on and supply a gnd to the lift motor solenoid and get the lift to go up and check your batt voltage under load. Careful if you go too high it will possibly break the limit switch on the lower right side.