Sarah, the two brothers must have been called up, so they must have military records. You could try asking for his military record. It has to be done by post to the records office in Glasgow, and it will cost you £30 up front, non-refundable, to have the search done. However if they find them it should be very revealing. You could do a similar request for his brother.
Dave
Edit. Conscription was introduced in May 1939 and the 1939 Register was taken on 29 September 1939. All initial conscriptions were complete by the end of he year so your 2 relatives will have been in army camps somewhere at the time the register was taken.
Hi
Clifford Smith's baptism is on this site and it gives his date of birth as 28 June 1919. Might help with any searches.
SMITH, Clifford (of 22 Albion Street, born 1919-06-28).
Baptised July 13, 1919, by J Trevor Lewis at St George, Brook Hill.
Parents name(s) are Emily Winifred & Charles (Carpenter).