I've only repainted 3 of my signals, and left the insides more or less alone on them all. On my TSI's, I even left a little bit of the original dirt in there too, since there wasn't much to begin with...
But you said "a quality restoration". Given that, I'd want them to go back as close to the same state they were at first -- painted, bare, or 'overspray' -- however they were made originally.
Spoiler:
now don't y'all go hating on me for saying this -- but that's one thing that often 'bugs me' just a little bit everytime someone gets a gorgeous new powdercoat (or etc) paint job on an old signal -- no matter how admittedly fine it looks all fresh and shiny new on the insides...did they really come outta the factory like that??
I spoke to a traffic technician guy a few months ago who was replacing 2 eagle flatback clusters with what I think were GTEs and he showed me the inside of one before installing it, it had a bit of overspray from when the outside was painted but no paint otherwise. Based on this and my own preferences, I'd leave the inside either unpainted or whatever paint was there to begin with, just as a reminder of what's under the outside coat.
The only reason the factory didn't was to save time and money. Both reasons are insignificant when compared to the weathering that could happen if you leave it unprotected.
My signal was painted inside and out. I've restored several national winning cars and just can't leave anything bare metal. I don't want to deal with rust, etc.
What I'm doing on mine may not be 100% correct...but here goes. I'm doing this fixture in green (which I understand is period correct).
For the doors and body, I'm blasting the parts to bare metal...then spraying the insides with Seymour stainless steel spray paint. They also make Alumablast and Cast Blast. Anyhow, after spraying the inside with the steel color...I do the outsides in the green. Some green gets onto the insides...but I think it looks authentic. I can't imagine a company spending the time to mask off the insides.
I guess I may be putting too much car-resto thought into this. When there's a question in my mind about how a maker did something...I always think...."what was cheapest and fastest?"
I've only restored CH but I had all the parts apart when I sprayed. I could have turned a blind eye to the back side of the frames but I certainly sprayed the back side of the doors. It would be a pain in the neck to get the inside of a light that has a 1 cast body. Even then I'd still spray the back side of the doors
I'd say if you are going for a total restore, I'd paint the inside, but if it is just to make the outside look better and it's not really a restore, but a touch up, then I would not bother......Depends on the piece and where you intend to display it...