It looks like it would work, but you've got a lot of wiring to do- it's not going to be anywhere close to 'plug-and-play'. According to the relay's specs, one 'pulse' of current from the stalk switch will close the relay, then the next will open it. So going into the spring-loaded stalk switch position turns on and leaves on, as doing that agin turns off and leaves it off. There's a parasitic drain on the relay control circuit, so power for it will need to come from a switched 12V source. That will need to be fused.
Personally,l I'd just hack the existing wire and add a SPST switch somewhere for the rear light as a cheaper and easier solution to implement and to easier to reconnect when I sold the car. But that relay seems like it will give you the functionality you seek if it's wired up correctly so the choice is yours.
Phil