It's gonna be the wiring on your reverse light switch, which is on the transmission. It's probably a different plug between the automatic and the manual, or maybe whoever did the job just forgot to plug it in. Look for an empty harness connector dangling off the drivers side of the transmission and another one poking out of the body harness near there. If they match, plug it in. If they don't, you might get away with splicing the correct connector onto the transmission, it's probably the same wiring. Or take it back to whoever did the swap and tell them you need it done right.