Yes, I have the exact same problem. In fact, it's a very common problem.
Search for multi-function switch or fog lights in this sub-forum and you'll see lots of posts.
By a new multi-function switch somewhere between $50-120 (depends on year and seller). Search the write-ups on multi-function switch replacement here on the forum. There's a relay on the old part that has to be transferred to the new part.
Rewire a new fog light switch on the dash in an empy or unused slot. This is a lot cheaper solution and avoids sinking money into a part that malfunctions a lot. Search the write-ups for fog light replacement here on the forum. You need to remove a couple wires from the MFS and hook to your new switch in order to keep the same functionality (only turn on when low beams on, etc).
I wonder if I can find a switch that looks like the originals just to maintain the overall look of the interior.
At $80-120 for mine, I'm thinking of disassembling to see if there's an easy fix (not likely) or doing the rewire. With only a soft top, the rear defogger and rear windshield washer slots are kind of useless, plus I have an empty slot, so I have some choices.
As to the replacement MFS, replacement parts are often a lot more dependable than the original parts once a defect has become obvious. Don't have any feedback on how long the replacement switches have lasted, since rewiring to a switch on the dash seems to be the most common choice. A replacement switch is a bit of a gamble (but what percentage of the original parts actually fail - you only see posts of failures; not posts about how happy a person is about their turn signal indicator/fog light switch) while the rewire is a sure thing.
In the meantime, turning the right blinker on or the left blinker on once the car's turned off prevents the switch from draining your battery (just don't forget or you'll be looking for a jump once again). Alternatively, you can disable the fog lights as you did.