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I think you're going to find a ground somewhere to be the issue.
Since you just had a frame off restoration, I would bet money a ground is the culprit.
Check ALL of them. Make sure they were all replaced, and the grounding
surfaces didn't get coated with paint.
I went through this last fall. Pulsating lights.
In fact, when I saw your post, I thought someone had resurrected my old one.
Mine was easy though. Bad battery ground.
Sounds like a ground issue. The regulator grounds to the fenderwell, which is bolted to the firewall, which itself is grounded to the engine block through a braided ground strap. Without a ground strap, problems like this start happening. You can temporarily test this by running a ground wire from one of the regulator's mounting bolts to the engine block.