Hi, Sam -- That little bit of information helped a lot.
There are two areas of the battlefield that have markers and are fenced or gated. The fenced area is near the monument and has markers where various members of Custer's Column fell. Some are marked with specific names; others simply indicate that a member of the 7th Cavalry fell there. Since James Brannon cannot be found in any of the 7th's rosters, it is unlikely that you saw his name on one of those markers.
The most likely location is the Custer Battlefield National Cemetery which is on the battlefield grounds near the Visitors Center. The cemetery is not fenced in, but its main entrance could easily be remembered as a fenced area. I checked the interments in that cemetery, and the closest name I could find is James Brennon. Go to www.interment.net/data/us/mt/bighorn/custernatl/cust_bjbz.htm to see his listing.
I hope I have been helpful. Please feel free to visit www.lbha.org and post a message on our boards if you want to explore this topic further.