I would start with testing the switches in the B pillar. Maybe it's wet from washing...

 

It's been a couple of weeks since the wash, and the F has been outside and in the garage during this 80+ degree weather. Pretty sure whatever got wet should be dried out by now, but I plugged in the fuse today and the puddle lights came back on and stayed on. What should I be looking for in the B Pillar?

 

There is a grommeted switch in each pillar for the lights. I would start there. There could be moisture in the switch causing it to short.