The pistol looks fine.
Tower Private Proofs ended in November of 1804. I think the pistol is later but, not trusting the proofs, I don't see any way to conclusively date it. Another possibility is that someone has "improved" a perfectly good original pistol by stamping it with the fake marks available from a well-known supplier of black powder parts. Needless to say, I consider this an encouragement to fraud. Supposedly, they are intended for reenactors but I've now seen those marks on several otherwise unmarked originals, including one sword which only proves how ignorant some people are.
I'll add that I have many examples of Tower Private Proofs...let me see if I can find a picture to post.