There is a John Andrew Wright from Edinburgh in the 'Royal Tank Corps Enlistment Records, 1919-1934' on FMP, which states he originally enlisted on 27 Nov 1914, then re-enlisted in 1920. I've no idea if it's your relative, but there's lots of detail in the image, including his occupation and his mother's name and full address, so you can check if it fits. I found my great uncle in these records and was able to confirm it was him because of his home address (which was the house where my mother was born!). It seems that Army Order 124 of 1919 offered financial incentives to soldiers to re-enlist - as a reserve force for ongoing peacetime military commitments following WW1 - and my great uncle signed up for 4 yrs 3 months (for which he would have received a £50 bounty – worth having in 1919!). It looks like your relative may have done the same (as many thousands did, apparently). I couldn't trace my great uncle's army record (presumably destroyed in the blitz) but this record gave his regimental numbers and so I was able to trace his medal card too.