Ken is correct, it has to be two problems occurring together.
If the battery is not at fault, and your time for fault-tracing is limited, you might do as I did and slightly loosen the battery ground cable lug and pull it off for overnight. In the morning pop the hood and push/twist the lug back on. If possible, listen for a relay closing when you make that connection - may be a clue to what's using power when it shouldn't.
Yes, you will loose radio presets, but it is a way to keep going for a bit until time for the detective work is available. One of the two relays in the power door locks can stick. Listen (have a helper) at the center dash air vents for a click when the cable is connected.
Tail lights are notorious for leaking. It's usually where the lenses attach to the lamp assembly. Look at the path the rain run-off follows: Down the rear window, collects in the trunk seal groove, washes on down to splash onto the top of the backup light and other lenses.
Check by (1) Push the car side-to-side and see if any liquid sloshes inside a lens, or (2) pull a bulb holder - I check the right side backup light - and look inside there or stick a finger in there.
Many bricksters have drilled a drain hole in the lenses that leak. Use a 1/16-inch drill and put the hole in the lower outside corner.
Good Luck,
Bob
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