I really appreciate all the suggestions from everyone. I popped over to a local vintage guitar shop in town on the off chance that they would have a similar headphone jack as a spare part. They had something very similar to I bought it for $7. As it turns out, the switching inside the jack is identical to the original. Even though I rang out all the connections on the old one, and everything seemed to be working, I went ahead and wired up the new jack and installed it. It ended up working perfectly. I'm guessing that perhaps the contacts internally were corroded, which may have loaded the circuit more than expected but that is a wild guess. Either way, I'm happy to say that the new jack worked.