Replacement stems for Lucas fog lights?

Isn't it just like a carriage bolt. I would think you could just get a new pair of stainless carriage bolts that size and length. Wouldn't that work, or is the inside of the light housing shaped so that that wouldn't work? This is just my 2 cents.

I would try the carriage bolt option first also. From the underside that's exactly what it looks like. The top might need to be modified depending on what the inside of the fog housing looks like, but hopefully it's not too bad.

Are these going on the higher pedestal mounts like the GT/CS cars or on the low square mounts like the Shelbys?

The rivets could easily be replaced, but you'd have a hard time finding the perfect replacement for the original. So upon VERY close inspection you might notice they'd been changed.

Another option is to grind off the backside of the rivets (your 2nd pic) and then epoxy everything back together again after replacing the carriage bolt. Keep in mind you'd have a hard time getting things back apart again in the future should you need to.

A 3rd option is to try and grind down the rusty bolt and get down to good clean metal. If you can do that (up near the fog base) then you could either weld an extension on or sleeve it (again with epoxy) You'll never notice the repair to the threaded bolt itself because it will be hidden inside your 3" pedestals.