Need to use 75 ohms to signal a 12 volt relay

I am trying to hook up a reverse light circuit on a project vehicle I'm working on. The vehicle has a resistor pack inside the transmission which changes the resistance through a signal wire to the speedometer ECU depending on which gear you are in, the ECU uses these signals to light up the different indicators on the dash telling you which gear you are in. The readings are as follows:

Park 24 ohms
Reverse 75 ohms
Neutral 160 ohms
Low 300 ohms
High 620 ohms

What I want to do is use the signal for reverse, 75 ohms, to activate a 12 volt relay for reverse lights but the relay can only be activated then it sees 75 ohms, not more and not less. Is this possible?? Thank you

Is the dash ECU gear indicator still connected to the resistors? If so that will affect how you do the sensing, since the indicator would already be applying a voltage to the resistors to determine their value.

What you need to do is measure the voltage across the resistors for each gear setting with the indicator connected. You could then use a window comparator to sense the voltage for the reverse position and turn on the reverse light

Or sense the reverse indicator light voltage and use that to power the relay.

Why can't you just tap directly into the rear backup indicator light? You can easily parallel a relay on that line.