Normally you would confirm military service before seeking membership in GAR.
Have you found his obit in Pa. , it may mention service in the military. If you know what cemetery he is buried in, their file may mention if he received a military funeral and perhaops if a GAR camp officiated at it.
I did a search of the 1890 veteran census for his name for Washington County, Pa and found...
1890; Census Place: Peters, Washington, Pennsylvania; Roll: 91; Page: 1; Enumeration District: 147. John Brown, Company "A" 85th Pennsylvania Infantry Volunteers. He served for 1 Apr 1861 to 1 Oct 1863. It listed his resident as Thompsonville, Pa.
This soldier was born in 1837 in Pennsylvania, so probally not your ancestor.