2007 Jimny how to remove back up light switch

The back up lights stopped working and I want to remove the switch to test it for continuity and to replace it if it has failed.
Due to it's location, I'm unable to get a box wrench over it and a standard socket is not deep enough to go over the electrical terminal and allow engagement with the switch hex.
I could purchase a deep socket if I knew what size I needed. Size not listed in the service manual.

While I wait for an answer here, I will jump the switch plug connector and verify that the lights work. Already checked bulbs, fuse, ground.

2007
Model SN413V
Type TYPE 6
JS3JB43V67430xxxx
Engine M13A
Transmission R72
2007 Jimny modification:SN413V-6 (E02,E05,E10,E11,E21,E22,E24,E37,E38,E42,E43,E54,E85,E90,E96)
TYPE 6

Jumpering the switch connector made the lights work, confirming that the switch has failed and will have to be replaced.  Hopefully without having to lower the transmission (gearbox).

Follow-up ... I purchased the replacement switch
37610-76G10 and the deep socket needed will be 21mm.

The socket will have to be cut so it is no more than 5mm long, otherwise it won't fit as the body is too close. Then you can use a small 8" pipe wrench on it. You will probably have to grind grooves so the wrench will have something to bite.

Sounds like a 21mm open end wrench might be the go here...

Or ring spanner if connector fits through it
I would also go with pipe pliers
socket would be my last choice 
To gain access you would need to remove gearbox mount, loosen engine mounts Jack front of engine to drop the gearbox down imo