Hi I just checked the Valuation Rolls for 1935 on Scotlandspeople for you and there is no Thomas McGee listed as living there. It is a very long street with lots of shops and houses.
However there is a Patrick McGhee living as a tennant at number 463 and a Gilbert McGhee at 762. If either of these were relatives of your Thomas then perhaps he lodged with them

Does the birth certificate give a house number on the birth certificate?
Dorrie
A warm welcome to rootschat from me too.