Something else you can check - the shift lever inside the cab. It has a wire type spring and rubber bushing inside that can be missing or broken. It also needs to be lubed with light grease but needs to be taken apart to do so.
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