Ed Gerdes transcribed Pipkins' service record from the NARA microfilm roll. It looks like Fold3 inadvertantly passed over his CSR when they were copying the rolls. I've been told that they missed a couple of men in the 3rd Arkansas, but I haven't had a chance to confirm that report.

If you check the CWSS index, you'll note that they list William Pipkins as having a CSR. You should be able to get a copy from the NARA roll at the Arkansas History Commission.