I remember that band too. They marched round, playing proper good old march tunes. The leader - I think his name was Albert Risby or Rigby, and he used to throw his stick high up in the air and caught it as it came down. We all hopes he'd drop it but he never did.I can remember the Beswick Prize Band at Maine Road.
Btw,if you support Hibs as well (as it says by your username) then you'll recall City playing Hibs in a friendly at Maine Road. Hibs won 4-2 and a player called Souness scored all four Hibs goals.