I was curious about the careers of the lesser-known people who signed the document, including that of James Breckinridge (in this document, his name is spelled with an 'e;' however, after further research, I found that it was indeed Breckinridge, with an 'I.' He was born in the area that is now Fincastle, VA in 1763 to a well-known, wealthy family. He served in the Revolutionary War before studying law at William and Mary where he studied under George Wythe. He then began his political career entering into the House of Delegates, then serving in Congress as a Federalist beginning in 1809. He served there for four terms before returning to the House of Delegates in 1819. In that same year, he was appointed to the Board of Visitors at the new University of Virginia, of which he stayed a part until he died in 1833.
https://www.encyclopediavirginia.org/Breckinridge_James_1763-1833#start_entry