That would be an NF-104A, serial number #NF-762. This was one of three modified "A" model -104's with "G" model tails operated by the USAF Aerospace Research Pilots School. These aircraft had an LR-121/AR-2 rocket engine... a bit different from a stock -104, but do-able with simple mods to a -104A kit. My uncle T.K. flew one in the late 50's...
Century Jets has a -104 kit, as does Avonds. Hope your "jet skills" are up to date...should be an exciting ride!
Barry