It reminds me of my father's Allan Glen's cap from a similar time. Certainly the colours are the same. It could be worth trying to contact the current team (or the school) to see if they can help.
School might be a unlikely - born in 1904 - so he would be 17 or 18. I don't know when he left school.However he was paying national insurance by middle of 1922. He also enrolled at the Glasgow School of Arts in 1922 - did they have a rugby team???