Introduction
The 1983 booklet "Gunsmiths and Gunmakers of Bedford and Somerset Counties Pennsylvania 1770-1900" includes John Baker in its list of Bedford County gunsmiths, puts him in Providence Township, and indicates that during 1777-1778 he was a contractor who was working for the Pennsylvania Committee of Safety.
I believe the inclusion of John Baker in the 1983 booklet was an understandable mistake. I think the gunsmith John Baker was actually in Providence Township of Philadelphia County, rather than Providence Township of Bedford County. The authors of the 1983 booklet did not include John Baker in their 1991 book "Gunsmiths of Bedford, Somerset, and Fulton Counties" or in their 2017 book "Gunsmiths of Bedford County, Pennsylvania". John Baker is included in this project so that the 1983 entry about him can be evaluated.
John Baker of Providence Township
The 1953 edition of the "American gun makers" compendium has an entry for a John Baker who was in a Providence Township in Pennsylvania in the 1768 to 1775 timeframe. The county is not identified. That is a problem, because Bedford County isn't the only Pennsylvania County that has had a Providence Township. When the 1983 booklet was written, it wouldn't have been easy to know that.
The following excerpt from the "Committee of Safety Musket Makers section" of Sawyer's 1910 book "Firearms in American History" may be the source for the John Baker entry in "American gun makers". Sawyer names the township, but doesn't name the county.
The following excerpt from the Volume III of the book "American Archives", Fourth Series may be Sawyer's source. The referenced Whitpain Township is in present-day Montgomery County. In 1784, most of of Philadelphia County became Montgomery County. Based on that, and the fact that Robert Morris attended the meeting, I think it is clear that the meeting took place at Philadelphia and the referenced Providence Township was then part of Philadelphia County.
The following composite image is from Volume X of "Minutes of the Provincial Council of Pennsylvania".
The following composite image is from Volume XI of the "Minutes of the Supreme Executive Council of Pennsylvania". It references a John Baker of Providence who was in possession of firearms in 1777.
The following composite image is from the 1778 map "A Chorographical Map, of the Country, round Philadelphia". It shows the then existing boundaries of Philadelphia County; one boundary was the Schuylkill River.
John Baker of Norristown
The 1953 edition of "American gun makers" also has an entry for a John Baker who made firearms for the state of Pennsylvania in 1776. This John Baker was located at what is now Norristown, Pennsylvania. The site of Norristown is between Reading and Philadelphia in present-day Montgomery County, which means it was in Philadelphia County in 1776. Norristown is also very close to present-day Lower Providence Township of Montgomery County, but is in Norriton Township, which already existed in 1776.
The following map from the 1884 book "History of Montgomery County, Pennsylvania" shows the locations of Upper and Lower Providence Township of Montgomery County relative to Norristown.
In the 1895 book "Historical Sketches..." the Rev. Charles Collins wrote "John Baker was an ingenious worker in iron, steel, and other metals. His father was a native of Germany; and a very early settler in the vicinity. During the Revolutionary War Mr. Baker rendered very efficient aid to the Whig cause, by his handicraft, in the work of repairing suitable fire-arms. Mr. Baker lived to a great old age; being nearly a centenarian; and died about 1820."
The 1953 edition of "American gun makers" reports that the shop and farm of the gunsmith John Baker were located on the south side of Germantown Pike at the intersection with North Wales Road. The following image from the 1950 Sanborn Fire Insurance Map shows the referenced intersection, which is at 40.14904764450116, -75.33478031379664. The 1953 book also states that John Baker's son Arnold kept the Barley Sheaf tavern and died on the family homestead circa 1858. The tavern still stands about 100 feet southeast of the referenced intersection, at 40.148566244919685, -75.33435252080639.
Arnold Baker's tavern is identified with a yellow arrow on the following markup of an 1857 map of Norriton Township:
An earlier John Baker of Lancaster County, Pennsylvania
A John Baker of the Borough of Lancaster died in 1750, and is mentioned briefly in Research Bulletin No. 21 of the Kentucky Rifle Association (1972, "The Baker Family Of Gunsmiths In Lancaster County, 1717-1754"), where he is described as a forger of gun barrels. To keep things interesting, present-day Lancaster County has a Providence Township!
An August 24, 1728 letter in the Taylor papers references "John Baker the gunsmith on Conestoga".
Lancaster County was formed from a part of Chester County, on May 10, 1729. The following item is from Vol. XIX of the 1915 book "Papers Read before the Lancaster County Historical Society":
Here's what the 1924 edition of Dillin's book "The Kentucky Rifle" says about one of the gunsmiths named John Baker:
The 1953 edition of "American gun makers" briefly mentions a John Baker who worked during the flintlock period in Lancaster, Pennsylvania.
Conclusion
I believe the John Baker entry in the 1983 booklet is mistakenly based on the John Baker of Providence entry in "American gun makers", and I believe that the referenced Providence Township was part of Philadelphia County during the Revolutionary War.
Click on this link for an index to biographical material about other Pennsylvania gunsmiths and the longrifles they produced.