The shop manual has trouble shooting info and a wiring diagram. You can dissassemble the solenoid and clean up the contacts. Many times the oil seal leaks and gets oil in the solenoid and causes it to short out. It can be cleaned up with solvent. The trans seal is available. Solenoids and original parts are hard to come by but many of us have found other components to replace the factory relays and kick down switches. There is a lot of info in this forum on overdrives.
Fred



1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine