1) It is possible, that the previous owner has hacked the wiring in some way as to have this all jacked up. If that is the case, well, you have three things to try:
A) Take it to a shop or dealer and pay $90 an hour for someone to guess or tear into the car and TRY. Expect this to be expensive and fruitless.
B) Get the service manual out and start reading; learn to use a DVM and learn about the difference between voltage, current and resistance and try to get to the bottom of this yourself.
C) Live with it as is.

2) and explain in detail why this happens.
Wow, Phil, poor form there. You are not coming across in a very good light.

Consider: None of us are here being paid to help anyone.
Why do you think ANYONE here has the time to answer in detail? No one here engineered the car, no one here knows what the previous owner did to it. No one here knows ANYTHING other than the few words you have typed. We see no photos, the battery condition, wiring, etc. are described by you; but all we have here is your opinion of what conditoin the car is in. I once went to look at a "showroom condition" car that the dash was looking like hell due to UV. Words really don't mean much.

Replace the battery and see what you get. If that does not fix it, and the car has always done this since you bought it, I'd say you may have bought one of those cars that some asshat tried to modify how the wing works. ANYONE who has tried that has failed, the operation of the wing is hard-coded into the routines in the BCM. If replacing the battery does not do it, I'd say this is something you must live with.

But you are wasting time not replacing the battery. That is the first thing to do in such cases. Look at it this way: Cost of a battery is the same as cost of about 1 1/2 hours of labor - no big deal.