The Mariachi peppers are dead. As a doornail.
It's probably all my fault. There are two things that can cause peppers to just wilt like this.
One is possible cause is Phytophthora Blight. According to Penn State, "Affected plants wilt and severly wilted leaves and branches die. Roots frequently are rotted. Under severe disease pressure, where soil is wet, entire plants can die rapidly." The description certainly matches the picture; however, I don't think it's this blight. The peppers are planted in a pot that had new potting soil - no garden soil involved. No other pot has had this problem, and they all have the same soil.
The second cause of rapid wilt and death of peppers is overwatering. As Texas A&M says, "flooding of the roots for long periods of time can also cause wilting."
And here is where I'm pretty sure I'm culpable. I have to water this portion of the garden in two steps. When I water, I use the sprinkler for 2-3 hours for each half of the garden (just once every 5-7 days). I think when I watered a few weeks ago I managed to mis-arrange the sprinkler so that it hit this pot in both watering steps. That would be about 4-6 hours of sprinkler action - not good. Because these self-watering containers don't have drainage holes (which would defeat the whole purpose) the pot became oversaturated with water and I just didn't notice until the plant started to wilt. And by that time it was too late.
The good news is that the Hungarian Wax peppers are doing great, and the Peruvian Purple peppers have just started to flower. At least I haven't been skunked.