I'm not sure it had much of a body. Although I couldn't find any pictures other than the one in the Georgano book, assuming it's the same vehicle mentioned in a Gamages Motor Cycles Etc. ad in 1919, it was described as The Tankette Super Motor Scooter, which implies a sort of Pashley-like trike.
A bit more research got this snippet from The Sketch, also from 1919.
The " Tankette " is a super-scooter with a seat two feet above the platform, pleasantly encased, and suitable to either sex, with a 3-h.p. two-stroke engine which will take you to Brighton and back on a single gallon of petrol at the speed of your own choice from one to thirty-five miles per hour, a most natty affair with two ducky little side wheels to prop you up in traffic, while your engine bobs on playfully, and a double-tyred back-wheel to prevent you from skidding into a motor-'bus or a ditch according to whether your environment be urban or rural. To and from the House of Lords or your ofiioe, according to the station to which Providence has called you ; a run in the country a week-end on your own, or in good company—-what better? No household, obviously, should be without several-—including at least one for the priceless general who commands the establishment and such a huge honorarium in these days days. - And the price ? Ah, that is the maker's little secret—as too frequently the case in these days. Iet us pray that he lay it on light for once !
