Really Strange Electrical Problem - 01 XJ

So I just bought my 2001 XJ Sport and I've noticed a weird problem with it, I can't explain it but....

When I am driving with my headlights on and get to where I'm going, if I don't turn the headlights off before turning the truck off the next time I go to start it it acts like it's completely dead. No dash lights, no turning over, anything. The only thing I've found is to get it back to life is to go jiggle the terminal wires on the battery then it fires up just like nothing happened. This ONLY happens if I don't turn the headlights off before turning the ignition off, if I turn the headlights off and then the ignition it's totally fine.

Now I know you're thinking "well just don't do that" but I'd like to figure out the problem because it could lead to something worse. Should I replace the terminal wires? They aren't very rusted or corroded so I'm kinda lost.

Sounds like you have corroded battery terminals and the rest is coinicidence.

Fix the known problem and see if the odd behaviors clear up as well.

Perform routine maintenance of the start and charge systems. Remove, clean, and firmly reconnect all the wires and cables to the battery, starter, and alternator. Look for corroded or damaged cables or connectors and replace as needed. Copper wires should be copper color, not black or green. Do the same for the grounding wires from the starter to engine block, and from the battery and engine to the Jeep's frame/body. You must remove, scrape, and clean until shiny, the cable/wire ends, and whatever they bolt to. Jeeps do not tolerate low voltage, bad connections, or poor grounds.

This^^. Do it before it won't start at all sometime.