Career
Fallon signed for Celtic from junior football team Fauldhouse United in 1959 to understudy for Frank Haffey and made his debut that same year against Clyde. He remained first choice goalkeeper until the signing of veteran keeper Ronnie Simpson from Hibernian in 1965. At that time the only substitute permitted was for the goalkeeping position.
As a result of winning the European Cup, Celtic entered the Intercontinental Cup later that year, a two-leg match against Racing Club of Argentina.
With Simpson unable to play, Fallon was called on to keep goal in a bad-tempered second leg, and an even more bad-tempered play-official Although Celtic lost the return leg, and the subsequent play-off in Uruguay, amid accusations of extreme foul play from the Racing players, Fallon distinguished himself with a string of saves which caused one commentator to remark: "If that"s the reserve keeper, what must the other guy be like?" According to Sir Robert Kelly in his book Celtic, when Celtic tried to get the second leg declared void because of the Simpson incident, Racing Club used Fallon"s heroic performance as their counter argument, and the result stood.
After Simpson"s retirement, Fallon took over as first choice at Celtic. He lost his place to Evan Williams due to a long illness, sitting out the 1970 European Cup Final.
He later played for Motherwell and Morton before retiring from senior football.