Well, so much for the microwave. As you said JG, easy to remove but nothing behind but empty, very dry wall. The vent exhaust is just below the microwave so nothing to see behind it.
Step two: On close examination via ladder the vent cover is not very flexible and held on by two tabs through the top and three through the bottom. All of them resisted any kind of movement with a flat head screwdriver. There is evidence of a very thin line of sealant across the top and the vent cover is away from the exterior wall in an area about 1/2 inch long by maybe enough to jab a fingernail between. Could be the source. I'm going to clean it and resort to a small amount of sealant and give it the hose test again.
On second thought I believe examining the vent hood beneath the microwave will be step two. It might not be too terrible to remove and the microwave didn't make me cuss.