I did a little more research on possibilities for "J. Bear". Here are 3 interesting finds of soldiers of the American Revolution. This does not indicate they are gunsmiths or gunmakers, but it does establish a connection to use of firearms in the right time frame.
1) Jacob Baer - a private in Captain Edelman's Company, 4th Battalion, Northampton County Militia.
2) John Baer - Class 6 in 8th Co. of Capt. Frederick Kuntz, Lehigh Township, Northampton County Militia, May the 2, 1781
3) Jf'hn Baer and Peter Baer - in Capt. Adam Staller's Company, Northampton County Militia OCT. 3TH. 1781. (c.)
I don't know if "Jj'hn" is an abbreviation or an OCR error by Google. If the latter, it could be "John," which could be the same person as #1 having changed companies, or a different "John Baer."
I also found reference to a "Baer Valley" near Seipsville, Weisenberg Twp., Lehigh Co. So many of the Baer family lived there that the locals called it the "Baer Valley." This is adjacent to the Berks County line.