Gidgee Stephens was from Broken Hill and was a well known motorcycle racing identity from there, he was the first Broken Hill lad to race at the Royale, the photo is probably taken somewhere on the western plains.
The Beezer is geared too high, going by the back sprocket, to be a pure speedway iron, so it must have a gearbox, there appears to be one fitted but it's obscured a bit by the " trailer " mudguard and wheel, it also has a tacho fitted and what appear to be Harley or Castle forks so its sidecar heritage may be there, plus it's carrying race numbers.
The frame appears to be a rigid BSA or Triumph , the seat certainly is, and the tank straddles the frame not slung beneath the top tube.
I think you are pretty right about the time frame , Firko, was thinking early '60s meself.
Very plurry interesting pic , would love to know the bikes history, thanks for posting it , Dutch
I must admit I did google his name but forgot to copy the link, interesting stuff
Foss
Here's the link
http://www.sportingpulse.com/get_file.cgi?id=1259207