I did not find a single Wiley Taylor. However, I found 2 "W.W.Taylor" serving SC. Both privates, one served in Company K of the 1st Infantry, the other record is with Manigault's Battalion of Light Artillery.

Also existing are records for 4 "W.Taylor". You would have to research all 6 to be certain you have the record of the person you seek. More detailed info might be available in the SC Archives.