Thanks for posting the pic of the back of the body. Looks like it has the deep tummy cut along with the router bump so it appears that the body is a genuine Fullerton vintage reissue. The neck where the rosewood meets the maple at the headstock also points to it being a Fullerton reissue.
I would think you'd be able to tell if the fiesta red is the original finish once you receive it and can pull it apart a bit. From what I've read, they did do some oversprays at the factory for colors like fiesta red so this story matches up.
I hope it plays well.
These Fullertons usually play really well. I just pulled my 1983 '62 P out of its case to compare the back body dimensions to your photo and have been playing it for a bit. It's been a while since I've played it and it is definitely a treat to play. As good or better than the Fender Custom Shop basses I've had.