Can you send pic of wiring? Switch on constant power line have a fuse on it?
In order to have reverse come on with reverse OR on command you’d theoretically need 2 relays...But you could move that switch to the “trigger” wire for relay (pin 86). *It does need to be fused!
I’m assuming there’s 2 red and 2 black and if you hook each up to a battery direct, it should fire. One circuit should be able to rely on reverse power, because that’s already a fused line with a relay. The on-demand circuit needs its own relay for longevity reasons.