Its most likely the neutral safety switch which also activates the backup lights on automatic equipped cars. If your shifter is on the column, its located under the dash on the column. If a floor shift it should be mounted on the shifter. It may just need an adjustment or it may be on the way out, or it may just need a good cleaning.
I bought a new Neutral switch from Napa (part #NS6410) which is the only one they had for 68 camaro, AT, 327 and it did not fit, they did not have one that specified column shift or not. On the first picture you can see the plastic 1/2 inch or so white tab is a little wider than the original (original part on bottom).
The second photo shows the bottom curve radius is different that original curve radius so it will not seat over the steering column.
I don't believe the switch has detents in it, it's just a slider. So as said, loosen the mount bolts, rotate the switch slightly (guessing clockwise), retighten and test. Repeat as needed. Adjust it so that it only starts in park and neutral, and the backup lights only work in reverse. Pretty simple, really.
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