I finally figured out what parts I need and ordered them. 4-6 weeks later (Or so it felt, really it was just 5-8 days, I didn't pay for expedited shipping) they showed up and I had some time this evening to get to work.

I got the header pins soldered onto the Arduino Pro Mini, programmed it with "Blink" to verify programming worked, then programmed it with my Christmas light sketch. It's pretty good the way it is, but if I want to make changes later on, I can take my laptop outside, open the lid on the case, and reprogram it.

I also got the Pelican case drilled out, the three cable glands installed, and the power supply glued to the bottom of the case. I weighted it down with a tape measure and BAW (big ass wrench) while the glue cures.

The cable glands are (L-R): input power (120VAC 60Hz in my locale), light string 1, light string 2. By center-feeding the lights, I get better power distribution, and the sketch is designed such that the two strings of 50 lights will behave as if it's one string of 100 lights.