Brian: Thanks for posting your question. Your "Thomas Parker" shotgun is
NOT a Parker Brothers made in Meriden Connecticut USA shotgun. Here are a few non-Parker Bros. guns that will show the word Parker on them somewhere. Parker Trap Gun, Field Parker & Son. E. D. Parker (Belgian), C. Parker & Co (Belgian), E.D. Parker (Belgian), T. Parker (Belgian), T. Parker New York (Crescent Fire Arms), Thomas Parker (London), W.Parker New Pin Fire (maker unknown) and Parker-Smith-Williams (maker unknown)
SOURCE
There are many internet references that discuss "Thomas Parker". Many references refer to "limited value" for a "Thomas Parker" shotgun. If you search for "Thomas Parker shotgun" in Google you will get information for your purposes.
Regards,
Jack