I recently went thru something very similar on my daughter's '02 SE wagon. The symptoms were slightly different (she doesn't have a green mileage indicator on this car), but the effects were the same: a brand new battery going flat overnight. A voltmeter reading in the evening showed 12.8-13.0 volts & the next morning it would be 11.6-11.8 volts.
The problem turned out to be a faulty
brand new alternator. I had to take the car to a specialty automotive electrical shop (servicing RV/campers & work trucks) in order to track down the issue. They identified the alternator as allowing voltage in the reverse direction (battery to alternator) when the car was off. They measured 4 to 6 amps of draw, & pointed out that the alternator would even 'hum' sometimes when the car was off!
Before having it tested I was disconnecting the negative battery cable at night & reconnecting it in the morning to keep the battery fresh. This was a bit of a hassle, so I installed a
battery 'quick disconnect' so that she could disconnect/reconnect with a few quick turns of a knob.
After having it tested I took the independent test report to the parts store & got a free replacement alternator. The first new/remanufactured alternator cost USD $140 & came with a 1 yr warranty. The electrical testing cost another USD $85, but it was worth it to know exactly the source of our problem & to avoid any hassles from the parts store.
After replacing the alternator again (
), a voltmeter test showed a solid 12.8 volts after parking overnight.