I put much of the finishing touches on the electrics of the BSA today. I have some LED headlight bulbs (could only buy a pair) on the way for it, so I thought I might as well get ahead of the curve and rewire the connector (which has seen better days and actually appears to have suffered a fire or at least overheated at some point). New wire up from the battery (which doesn't exist yet), new terminals for all the switches, a new ground wire, and then I hacked up the bulb connector and soldered two new wires to it because the old ones were very frayed.
I do still need to replace the dip switch - I confirmed today with a multimeter that it's very broken inside. I don't think they're particularly expensive though.
After that, I took a look at the clutch lever. It looks like the bike might have been dropped at some point, or at least bumped into something, as the lever and where it mounts to the handlebar are very bent and it's got a huge amount of play in it. I removed the lever, used a shifter to gently flatten out the mount, then squished the lever till it fit satisfactorily (though I haven't ruled out simply buying a new lever at some point - the two levers don't match and they're riddled with surface rust).
After adjusting the clutch cable to take up the slack, it feels excellent - I may not have to replace the clutch cable after all. Easy enough to pull and snaps back to open resoundingly, without catching anywhere.
Update: I went to Supercheap and stared at bulbs for a while... I can't find anything that looks like it'll fit for the speedo backlight (not sure if that's a RWC requirement or not), but I was pretty confident in the BAY15d stop/tail light bulb they had, and it was four bucks so I decided to give it a go. It fits perfectly, and after connecting a 6v dolphin battery to the system and checking lights I believe it's wired the right way around too.