The tail lamps need to be 3 wire style lamps. One for ground, one for brake, and one for running. If they are simple 2 wire lamps, then you need to replace them with the appropriate 3 wire lamps.
Your license plate lamp is wired into the reverse light circuit, and needs to be wired into the running lamp circuit.
My 5.2L Build thread
-1989 Jeep Wrangler 2.5L, soon to be 5.2L
-1996 Jeep Grand Cherokar 5.2L, donor and rainy day driver
-2004 Kawasaki KLR650 sunny day driver
"A well regulated Militia, being necessary to the security of a free State, the RIGHT
of the people to keep and bear Arms, SHALL NOT BE INFRINGED