Why? You would need to cut wires from the neutral start circuit and run a separate wire and switch to the lights. The previous owner of my 5th gen did that and it turned out to be a mess when all you have to do is clean up or replace the NSS . The Neutral Start Switch controls the backup lights. This switch is easy to get to if you have the 5sfe. The wiring plug to the NSS is prone to corrosion because it is located in front of the engine. I would check the plug-in on the switch before going any further. IMHO
Inhibitor switch is a different term than we/I use here in the US. The switch stops (inhibits) the engine from starting if the automobile is in any gear other than Park or Neutral. Why the backup lights are in that circuit is beyond me but I had an older Jeep that was the same way. Maybe someone else knows. Here's a Youtube link that will clarify somewhat. How To Adjust An Inhibitor Switch - YouTube
Hope this fixes your issue.
When I put the car in reverse the reversing lights won’t come on.
I can reverse the car fine just no lights. It’s not the bulb & it’s not a loss earth.
There must be a switch to turn the reverse lights on.