Was their military equipment designed with the steering wheel on the right? Did drivers in the American occupation zone drive on the right? What happened when a British vehicle crossed from the British zone to the American zone? Did they have any formal procedures or instructions to guide them? Were there any accidents or incidents that resulted from the confusion?
The British military purchased left hand drive equipment for use on the Continent. Initially, it was simply a matter of "that is what th Americans gave us", lend lease from the factory. Afterwards, equipment (mainly soft-skins) started being procured in both LHD and RHD versions. The LHD version generally went to BAOR and Berlin, the RHD vehicles to U.K. Formations. LHD vehicles would have markings on them in white lettering saying "caution left hand drive" for the first few years, but later such markings vanished. Vehicles did not see their entire service lives on the Continent, occasionally they could be rotated back to the UK. Example, this LHD truck on a U.K. Motorway.
http://www.hankstruckpictures.com/pix/trucks/len_rogers/2007/04/scammell-army.jpg
Such policies are not unique to the U.K. The Irish Army, for example, primarily deploys abroad on peace keeping operations. As a result, it too has purchased left hand drive vehicles, happily used in Ireland when not on deployment, https://www.resimars.net/data/media/1514/irish_scania_drops.jpg
As a side note, note that a lot of tanks such as the German Leopard are "right hand drive". This is determined by the turret crew configuration requirements (loader should be on the left, and he needs to access ammunition in the front hull, which means the left side of the hull has ammo, not driver).
