My reverse lights stay on all the time .

I have a 2004 Ford f 350 crew cab dually 4x4 6.0 desiel . My reverse lights stay on all the time . With truck shut off and the keys out of the ignition . I had to disconnect the battery . And then remove the reverse light bulbs before reconnecting the battery . So it wouldn't drain my battery . Does anyone know what it could be ??? I was told that the part that needs replaced is in the transmission ??? It has the 5R110W transmission in it . Can anyone please help or let me know if I can hook up a manual switch on my dash ??? Please let me know if you can help me out with this ??? Or let me know if someone can explain to me how to wire up a manual switch for my reverse lights ???