Re: 1963 mercury monterey S-55
My experience is limited to later 60’s and 70’s cars but I would think it wouldn’t be much different for your 63. Usually they are attached to the shifter mechanism. If you have an automatic column shift, you can find it attached to the top of the steering column, and it usually has a set screw that clamps it down. On the ones I have worked with, the back up light switch is combined with the ‘neutral saftey’ switch. I don’t know if that was mandated in 63 or not, but if it was and it was only an adjustment issue, you’d have to move the shifter away from the normal positiion to start the car. If you are experiencing this then you might be able to simply adust the switch.
If you have an automatic shifter on the floor, the switch should be
attached to it, you will probably have to remove the console or a plate
to gain access to it.
I’ve never dealt with manual transmissions but my 65-72 parts book shows a switch for 65 mercs located near the shifter. It looks like a plunger that you would push against when you move the lever over to reverse. I am not sure where it is located if you have a column shifted manual transmission. That linkage has always been somewhat mysterious to me. I know it works, but I haven’t a clue how.
Once you find the switch it should be a simple matter of jumping the contacts to verify the switch is bad. If ‘neutral safety’ is part of the equation, you’ll have to figure out which wires are only for the backup light function vs. the starter function.
I hope this helps!