http://www.anti-aircraft.co.uk/polstenquad.html provides some clues. It mentions the Skink, which suffered extinction at the hands of the Allied Airforce, which gained air supremacy over Europe (and thus reduced the need for ground based air defence - many units were converted or re-converted to infantry units). Given the overall weight of the full up configuration (6895lb) I suspect that a C60 Cargo truck would have been the prime mover. It would make sense that a LAAT (light anti aircraft tractor) would be a good fit for this gun as the truck is configured for storage of tools, ammunition and personnel.
Other than that, I found nothing definitive (yet). I am looking for the book by a french author about Canada's Army in WWII - it has organization charts that indicates vehicle/weapon system paring.