I just read your reply, even though its been six months. Thank you so much for this information. I was wondering if your book (?) lists any additional information about William Williams enlistment record? You said it didn't give a place of birth, but what about a date of birth?
As for the "pension case," I suspect this is a reference to William's bounty land warrant application. William himself never had any children, and I assume was unmarried. His mother and half-siblings were his only heirs. Thus no pension would have been permitted for his heirs. But his mother and half-siblings did apply for and receive bounty land through William's service under the Act of 1842. But I still don't know why it says "Pension," you would think it would say see "bounty land warrant application" or something similar.
If you can provide any additional information, please let me know.