You clearly have a multimeter, so here is a structured fault finding procedure.

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1.

Select reverse, put in the correct bulb.

measure the voltage from a GOOD chassis earth bolt to both wires going to the reverse light.

If any one of them reads 12v, then the fault IS either the earth for that lamp, or the bulb socket it's self.

Assuming both read close to 0v:
2.

Find the reverse light switch

(Gearbox) and bridge it out
Does the light come on OK?
Yes

- replace switch
No

- continue

3.

Attach wires to a representative reverse light bulb.

connect one wire to a GOOD chassis earth bolt, poke the other wire into the two socket holes on the chassis loom that plugs into the reverse switch.

Bulb lights

- the fault is in the wire from switch to reverse bulb socket
Bulb does not light

- fault is in the wire from the ECU-IG fuse and the reverse light switch.

paul