I got a kit a few years ago for my ’63 Cutlass that was made from materials that are compatible with the crappy fuel we get these days. I can’t find the receipt but I think it might be this supplier I found on the net. Here is a link. Check with him to see if he has anything for your ’62 Jetfire.
I put an N.O.S. fuel pump on it shortly before that and it failed after about 200 miles. The rubber had deteriorated and the diaphram was torn when I took it apart. Rebuilding with new parts is the best way to go.