Parking lights and the Car Battery.
It was (and still is in some circumstances) a legal requirement to display parking lights on some roads, for times when your car is left parked in the dark. Some schools of thought believe you should never leave lights on as it will drain the battery, others say that’s the whole idea what the CB Ampere/hr capacity is for because it's being recharged. Then there are some cars with ancillary electrical equipment (alarm, clock, cellphone etc) which when left drain current which over time can add up to a significant A/hr drain. Let's do some sums, say the current is 0.05A, over a 24-hr period that's 1.2 A/hrs, after a week it's over 8 A/hrs. Whatever the situation, there still needs to be sufficient capacity to left start the engine (see above), a CB with reduced capacity will then fail at this point. Don’t forget a battery with greatly reduced capacity will still happily start a car, providing there's at least one A/hr left out of the 40-50 or so original A/hrs it had when it was new!
Above stolen from:
http://www.far-out.demon.co.uk/cardiy/battery.htm
I wonder if maybe your battery isn't getting fully charged when it is running. Measure the voltage across the battery when the engine is running. It should be 14 to 14.5 I think. You might be charging your battery only to 20% capacity and the "normal" parasitic drain is killing it overnight, where if you were charged to 100%, it woudn't even be an issue.
Measure the parasitic current in another vehicle. If it's roughly the same as yours, you're chasing a ghost and your problem isn't the drain current, but the charge state of the battery.
Another thing I've run across is a dead cell in a battery. If you roll the starter for a bit, but don't let it start, you should still measure over 12V. Close to 10V after rolling the starter indicates a dead cell (2V per cell on a lead-acid battery).
Good Luck!!