This is on a 81 F100 with the SROD transmission. I have checked the switch for proper operation in and out of the truck and it works as it should. When it is screwed into the plate it goes in which is indexed the lights now stay on all the time. This just started about a week or so ago. Before that they where working as they should in reverse only. I am just not sure what is going on in the part the switch screws into that is now keeping them on all the time. I have not taken this plate out yet like showing in the pic.
The circuit is shown on Page 46 here: Electrical/EVTM/1981 EVTM/Lights. You pretty obviously have power to the switch on the pink/orange hash wire, but you should check. And you apparently always have power out on the black/pink wire.
But if you go to Page 48 you'll see that it says to check the adjustment of the switch if the backup lights stay on.
Dad's: '81 F150 Ranger XLT 4x4: Down for restomod: Full-roller "stroked 351M" w/Trick Flow heads & intake, EEC-V SEFI/E4OD/3.50 gears w/Kevlar clutches
Blue: 2015 F150 Platinum 4x4 SuperCrew wearing Blue Jeans & sporting a 3.5L EB & Max Tow
Big Blue: 1985 F250HD 4x4: 460/soon-to-be ZF5/3.55's & EEC-V MAF/SEFI
The pic above is from the shop manual I have. I have see nothing referring to a locknut. It has worked just fine since about 1990 just the way it is. I was just thinking maybe something in the trans itself has changed or become worn maybe. The pic above looks identical to what I have plate, snap ring and switch.