I have just looked again at the Military record for Thomas Graham.
I think I am understanding this correctly, but on the page after his 1924 letter with address Stoneyhill Cottages, there is his discharge details.
The address on there is the address, 23 Saughton Hall, Murrayfield, Edinburgh. - 1919
There is then an address 30 Forth View, Wallyford, Midlothian which might be Musselburgh?
On a conduct sheet, it says he is 24 yrs, 5 months , was born in London, is a Footman and enlisted in Birmingham. Another page says he joined at Stirling.
Some of these details have been mentioned, possibly, but not sure about those two addresses.