That sounds very similar to what I was dealing with on my 'SD. For a brief while I installed one of those Priority Start batter saver things; it worked reasonably well by extending the battery drain intervals. However, in the end, the best thing I did was spend 30mins to isolate the draw from the fusepanel. I used a simple test light attached to the battery negative after disconnecting the negative lead, and touched every fuse (do a google search for instructions if needed). The one that lit up was the one with an open short. Once I narrowed down where the short was, I looked at the fuse panel guide to isolate which accessories it runs, and individually unplugged those, then retested with the test light, until I found out it was the power antenna.

edit: make sure you don't have any open doors, since those will mislead you as open shorts. If the hood light works, unscrew the bulb for this test also, or else it will appear as an open short.

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