It turns out that this is a pepper weevil.

I found a dead branch on the green pepper plant, and when cutting the branch, I got down to the hollow core where there was a small insect.

Here you can see the "woody" texture to the green pepper branch, along with the hollow core for of the branch. The core was actually filled with something like saw-dust. Presumably, this was eatten by the insect, and the sawdust was its waste.

While looking at this under the microscope, it started walking around. I was able to get a video of this thing waking up and walking around.