Circuit / component design help needed

I did not try and connect it to the other circuit. When I peeled back the insulation on the wire for reverse signal, and when I measured voltage present, I was thinking it would damage or mess up the other circuit Im connecting it to. Defiantly don't want to fry anything

The circuit I need to send the signal to is the Instrument cluster, when it gets ground signal, the cluster transmits a message to another module and it turns reverse lights on.

I've coded the cluster from Auto to Manual transmission and the reverse light diagram for manual transmission is:
Ground -> switch mounted on transmission -> to instrument cluster
When reverse is selected, switch closes and sends ground to cluster, otherwise open.

So, I just need to tie in to the reverse wire that turns the LED on, but I only want to see ground or open circuit on wire i tie in (so I don't damage the instrument cluster)
clint