Thanks to everyone that responded. Turns out that the ceramic/plastic bit that screws into the fixture was not screwed in well; so the bulb's cap was not making good contact with the socket. Doh!
Issue solved - thanks again.
To be clear, I don't know what I don't know about lighting and electrical, but this one seemed a little too straightforward not to attempt to DIY.
I have 2 single bulb fixtures in my garage that are controlled by 1 switch. I'd like to replace 1 of the lights with a ceiling fan. The single bulb...