You might think Revolutionary War pensions were started in the late 18th Century. However, in general that was not the case. Some states did initiate payments then to disabled veterans and occasionally to others. For information about those, the documentation would be found mainly at the archives of the individual state. However, the majority of pensions were not awarded until the early 19th Century. It was only then the the federal government got involved.
The first major pension act for the assistance of veterans, their widows and some other dependents was not enacted until 1818. So many pensions were approved that Congress had to appropriate additional funds. However, many applications were at least initially denied. As a genealogist, you should hope that the application of your ancestor was one of the latter. Applications that were immediately approved generated very little paperwork. Denied applications, on the other hand, sometimes resulted in voluminous files of correspondence back and forth which is often rich with genealogical information. Some of these applications disputes extended well into the middle of the 19th Century before they were resolved.
These pension applications files are housed at the National Archives. The easiest way to access them is through Footnote.com. Footnote is a pay site. If you are not going to use it frequently, you may wish to look for a nearby library which subscribes. Most local Family History Centers of the LDS Church hold such subscriptions for their patrons as do some public libraries. Check with you local library or family history center for information.
According to a newspaper article published in the Star of Christchurch, NZ in 1902, there were still three widows receiving pensions based on the service of their spouses during the Revolutionary War.
Among the jewels I have found in Revolutionary War pension files is the only official confirmation I have been able to find of the parentage of my 3rd great-grandfather, Peter Dowell, who was born in 1788. His mother initiated a request for a widow's pension in her old age. It was denied several times but Mary persisted until her death in 1853. A few weeks after her death a notice came that the pension had been approved. Then the amount approved for her had to be paid to her surviving children which were listed as Peter and his sister Elizabeth (Dowell) Johnson wife of Ambrose Johnson.