2006 Chev Equinox Gets Dead Battery If Left To Sit More Than 3 - 4 Days

I have a 2006 Chev Equinox which I purchased new in 2006.  I have approx 75000 miles on it and it is in excellent shape.  However, for the past year and a half the battery goes dead if it is left for more than a week.  The time frame can vary from 4 days to three weeks but it always drains the battery when it sits for any lengthy period of time.  I replaced the battery  --  no help.  I took it to the nearest GM dealer and they checked it over for a draw and found that the radio was drawing but not all the time.  It was very erratic.  They suggest replacing the $800.00 radio !!! I refused and found that if I turned the radio OFF before turning the ignition off the car could go for about 3 weeks.  Last week, it would not start after sitting for one month so we charged the battery overnight and it started fine the next day.  I drove it about 25 miles and left it sit for a 2 hour appointment.  Then when I opened the driver's door to get in the bell started to ring as if the key was in the ignition -- which it was not.  The only way to stop the bell from ringing was to close the door.  The car would not start.  There was no click or sound and it was completely dead.  I called the roadside assistance and it would not even turn over with a battery pack.  I had it  towed back to the GM dealer who had to leave it sit for three days since I did not have an appointment.  They then charged the battery and said it tested fine, the alternator tested fine and they could not find any abnormal draw anywhere.  They kept it for two weeks and the battery was fine and they had no trouble starting it.  There only suggestion was that it could be the ignition module or else another module that controls the radio.  Since they cannot find proof of it being either or those modules or something else, they suggest that I not waste the money on replacing either of these modules.  They now suggest that I turn on the turn signal before I shut the key off and this will close that loop.  Has anyone ever heard of this? I am totally frustrated.  If I go to another dealer or mechanic they will charge me for checking everything again.  I need to depend on this car and would like any suggestion that will help.