yes you need a switch, in your old application your switch was on the steering column or on the floor shifter. either way the wiring was routed to the behind the dash cluster to a plug that then routed it to the backup lights. Now you will have to run it from the transmission linkage to that plug that is behind the cluster. in 65 the switch is mounted on the tranny housing and has a hard linkage that moves the switch. the linkage runs from the reverse linkage to the switch. you will more than likely find an extra hole on the plate that mounts the reverse linkage to the tranny. that woud be where you hook it up. On a more modern tranny you may find the switch inside and a plug sticking out the side of the tranny.
Good luck, this may be a pain but it is important that you finish this for the safety of others.:nono:
The automatic had the backup light switch/neutral start switch at the base of the steering column. You need to add a switch to the tranny that is activated by the reverse shift crank. They make an on/off switch that has a ball bearing 'lever' that is perfect for this application. More importantly, you need to add a neutral lockout switch to prevent starting the car in gear. DIY by Use the common GM brake light switch that is on the brake pedal ar. Just adapt it to the clutch pedal arm on your car.
Or better yet, check w/ a GM dealer for the factory parts to do this!
I agree with willy36 don't ever disregaurd safety devises. They were designed for a reason. You are building something that everyone can safely drive because sooner or later you will let some drive it or you could sell it and it is of greater value if it is safe.
A '65 GTO didn't have a clutch switch. No car that I know of had one until the very late '60s. I bypass it on any stick-shift vehicle I own, because I feel safer without one. Probably something to do with seeing a car that got hit by a train because the driver killed the engine on the tracks & couldn't restart it (he got out before it hit). But then I drove sticks exclusively until I was ~35 years old, so I'm used to starting in neutral & using the parking brake. And I don't have a garage with a door.