OK, I figured it out.
As you know, GPS signals are weak and can be blocked easily. Whenever we drive into our basement garage, the heading indicator turns red indicating the loss of GPS reception.
First, I tested a metal clipboard by holding it over our handheld GPS unit. It blocked all overhead reception.
I put the metal clipboard over the square on the dashboard. The square does look like a patch antenna. It is not. GPS reception stayed green.
Next I tested aluminum foil by wrapping a single layer around our handheld GPS. It blocked all reception.
I wrapped the AM/FM radio antenna with 3+ layers of aluminum foil. The antenna does have an unusual spiral, but it is not the GPS antenna. GPS reception stayed green.
Then I put a single layer of foil over the top of the windshield. Some cars do have antennas embedded in their windshields, but I guess this is just a defroster. GPS reception stayed green.
I was stumped and was just playing around with foil on top of the dash when I noticed the heading indicator occasionally turning yellow. When I put a single layer of foil over the unit (but leaving the little square uncovered) and used another single layer of foil to form a hood over the LCD display, GPS reception immediately turned yellow and then went red. The GPS antenna is either in or on top off the Visteon Navigation Radio.
This isn't a great place for the antenna because the roof blocks a good portion of the sky. However, it does seem to do a decent job and it can apparently receive at angles you might not expect (like through the side windows). If the reception isn't good enough, the obvious solution would be to get a GPS reradiating antenna and put the external antenna on the roof and the reradiator on the dash on top of the navigation radio.
Now I better put the big ball of foil in the recycling bin before my wife sees how much aluminum foil I used in my experiments...
Lloyd