Reverse lights

Hi my 62 comet reverse lights flick on for a moment then stay off. Car has a 170 with mer o matic on the column. Gear selector is loose and worn but stays in gear. Shop manual mentions neutral/safety switch that can be adjusted but i am not sure thats the problem. Any suggestions for a fix appreciated

Fixing the slop in the gear selector should help it a lot. Ie the bushings and other wear etc. Good luck

Ok great i will focus on the slop. Thanks for the tip!