Start with the battery. Regardless of what the generator/regulator are doing (unless it’s going over voltage), the battery should not allow the avionics to reset. It sounds like it is low after starting, too low to keep the other systems alive. On an 8 year old battery, I suspect it is failing.
If you want to troubleshoot the generator, it can be difficult when it is intermittent. I just lost my generator in-flight a few weeks ago and decided to go with an alternator conversion because it saved time and was an upgrade.
The first things to check, if troubleshooting would be the output voltage at the regulator, the generator belt tension, and the generator brushes. If all that checks out them pull the generator and bench test it.
If you don’t find the problem right away, keep a close eye on your ammeter. If you get zero or discharge in flight then your generator is intermittent and will eventually fail. Brush up on your electrical failure emergency checklist, which is pretty easy on a ‘65. I was glad I had a handheld comm when mine failed.
I hope this helps. Good luck!