Spoke to a friend who runs a B&B in Pymouth. He says there are some graves, both Union and Confederate, in the Episcopal Church yard. Also said there is a man at the Port O' Plymouth Museum, Harry Thompson, who knows of 3 large grave sites in the city from the Civil War era. This info is apparently very guarded for fear of pilfering. Perhaps you could make your case to Mr. Thompson.
What unit was your ancestor in?
If I can be of further help feel free to contact me.

Regards,
Jim Baugh
surveypunk@embarqmail.com