Replacement Backup monitor OK but won't come on when reversi

you did do all this testing with engine running ? right
so that the tranny actually shifted to reverse
you did say the BU lights come on

it would seem the "trigger" wire circuit has been broken, it should be connected to the trans reverse that turns on the backup lights
you could add a wire from the BU lights, let it activate a small relay
but the relay in circuit between the HOt red and the monitor reverse turn on