Well Andy it is good you found the issue. And it is also good you posted a picture..
The photo is IMHO something horror stories are made of. Those solder joints look down right scary and likely dangerous.
YOU should have used crimp connectors like use on the two good connections in this photo.
My suggestion is purchase a new switch and a crimping kit cut and strip the wires and redo the connector.
The alternative is learn to solder and resolder the joints.
I have over 10 years experience in electronics industry doing repairs . I know enough about soldering to make a good joint and know what one looks like. the joint should be mechanically sound and electrically sound the solder should be smooth and shiny with no access.
There are many good soldering tutorials out there look for the ones from nasa and industry on you tube.