Generally a TH350 trans will have a shifter attached either to a column shifter or possibly a floor shifter. There is also a kick down cable connected to the carb linkage and the front left side of the trans case. A vacuum hose from the engine to the modulator located on the right rear of the trans.
There could be a backup light switch on the left side of the trans and on later 350 "C" transmissions a torque converter lockup switch. Possibly the PO installed an aftermarket neutral safety switch which would be attached to the trans pan and connected to the shift linkage.
Those are the only electrical components I am aware of on a 350 transmission.
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