I would suspect that Wiley enrolled sometime in 1863 or after, however, from these records, we will never know.
I would suggest, checking the pension applications from the state he resided in later in life. However, his letter indicates he to be a rather articulate chap. This would suggest to me, that he would have been relatively affluent, thus not eligible for a pension, which applied only to those indigent.
There is one other avenue to run down, and that would be records of the nearest United Confederate Veteran (UCV) camp from his residence. He would most likely have been a member.