Truncated video sample!
The Amazon & early 140 gearboxes have a spring contact at the back of the selector shafts which gives an earth contact for the relay when reverse engages.
Over time this spring either permanently bends or shears off, leaving you without the reverse lights.
Replacement is pretty easy for the M40, although it is "gearbox out" for the M41 overdrive unit.
Amazon, 140