The rain sensing wipers cannot be dealer adjusted. The fix for all issues is to change out the sensor, the stalk, BCM, software, or combination of all.
There is a sensor on the rear of the rear view mirror, and for that matter there is another on the front side. These are for the self-dimming electrochromic feature. It uses forward and rearward light levels to dim (or not dim) the mirror. In other words, remove the mirror and your rain-sensing wipers will still work.
The rain sensor is a small black reclangular box attached to the windshield itself. Its more visible from the passenger side. From outside of the car, you will see a circle with the sensor below, inside the glass.
With:
Without:
With that, there are 3-4 different windshields for the 07+ Expedition. Some sources suggest the 2007 model year can use the 2008+ glass where others suggest otherwise. The biggest driver is YES/NO to rain sensing and if its before 2015 or not:
Windshield 2007 7L1Z 7803100 A
Windshield 2008 & up AL1Z 7803100 A
Windshield w/rain sensor 2009-2014 AL1Z 7803100 B
Windshield w/rain sensor 2015 & up FL1Z 7803100 A
Not sure what issues could arise from the wrong windshield being installed. Places like Safelite **usually** only carry the most common, so if your glass is a replacement - did you get the right one?
Sorry to be so nerdy on the subject.
On a side note, I recall a discussion on an Infiniti or BMW forum I frequent. Had to due to repellents such as Rain-X, Aquapel, and others. Supposedly and allegedly these products increase the frequency of the wipers action as they somehow turn one normal-sized rain drop into a dozen smaller ones. As the dozen smaller ones pass by the raindrop sensor, the system thinks there is more rain than their actually is. Or something along those lines, its been a while since I followed the topic. It seems like auto detailers also sometimes use paint sealers on glass, and this results in the same. And I also learned even if you don't apply these products yourself, many carwashes use them in the automatics and I guess there even wiper blades & washer fluids now that apply the product.