From what I've gathered from reading around, the 2 speed axle gave alternate 'half gears' so the 4 speed box became effectively an 8 speed box offering a lower crawler gear and better economy over a range of terrain as a more suitable gear ratio was often available, both very useful to LRDG Patrols.
However I would have expected it to be detailed in the specification, with the only possible reference being the 'Speedo adapter' which would be necessary for more accurate navigation during the day, until a star fix could provide accurate co-ordinates at night.
Looking at period photos of LRDG trucks the 2 speed handle shows up whenever there is a suitable angle of the cab, which admittedly isn't often!
So until proved wrong, with the photographic evidence, and the obvious advantages of having this feature on the trucks, a reference to speedo adapter (which could admittedly be to do with the larger sand tyres) in the specification, Tony Smiths very positive identification of the feature ( and other features!) I am happy that 2 Speed Axles were a standard and beneficial feature of 1533X2 trucks.
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