Unless the wiring on your 62 is defective, or has brittle wire covering, it will handle the 78 amps just fine. Unless there is an issue, you won't need 78 amps very long, if ever. The extra capacity is a nice perk that will ultimately recharge your battery faster after a long draw.

There is a lot of talk about the bulkhead connection, and the amp gauge bypass. Does your 62 even have a bulkhead connector? It seems to me that the 62 was before the famed bulkhead connector, and was also produced with a real amp gauge. I also believe the headlight switch (or the ignition switch) was the primary voltage source on the 62, not the amp gauge like the later models of the 60s era cars.

Upgrade to the dual field 78 amp alt and the electronic voltage regulator (well grounded) and enjoy the ride. That system will last for years. Gene