I am working on building an old Raleigh Grand Prix and the rear derailleur was extremely rusty and didn't move freely. I disassembled everything, got all of the rust cleaned out, polished the cages, and greased everything with no issue. The problem came during reassembly. I over-torqued one of the allen bolts and broke the attached return spring. I couldn't get any pictures but.

Is there a resource for ordering replacement components for vintage parts or is it going to be easiest for me to just replace the whole derailleur?

It's hard enough to get small parts for modern, current derailleurs. For vintage, it's nearly impossible. Post your request, including all the specifics on model and vintage, along with photos, on collector sites, and you might find someone with a non-repairable derailleur with that part intact, who might cannibalize and sell it to you.

If it is one of the simplex models with plastic bits; you may be better off finding a different brand; period correct replacement derailleur. Even if the plastic (delrin? Bakelite?) is intact, it's just a matter of time until it fails....

That's what I was thinking too. Those delrin plastic Simplex derailleurs were well known for wearing out their body bushings. The common replacement during that period was a Suntour VGT. Those had a long sales service life and were built quite solidly so I'm thinking one should be much easier to find.

I figured that's what I'd end up doing. I was hoping to keep everything as is just to keep from spending any money on this bike since I got it for free to begin with.

There were several terrible components in the '60s-'70s; Mafac brakes were at the top of the list but the red label Simplex plastic RDs were right up there.

Replace that with anything and you will have made a significant upgrade...

Is there a bike co-op near you? If so, a salvage derailleur is all you need; friction shifting will work with almost any common derailleur, vintage or modern.