If this is EIFS and installed in 2016, it should have drain holes or a drip tray. Did you see any way for water to drain? If not, it may have been installed the old way, which was problematic.
I did not see any way for water to drain. The stucco was run below ground level, which is wrong, so I could not see the bottom. On the roof parapets the stucco runs down to the gravel and tar paper with no gap, so again, no weeps visible. I spoke to the owner since I originally posted this question and he said when it was re-stuccoed they power washed the stucco and then applied an new layer of stucco. I am beginning to think it was applied with 1985 techniques and then just a new layer of finish coat applied. This picture shows the section of roof the stains are on.
Power washing EIFS can drive moisture into the foam board at the fastener points. That’s why one should never pressure wash EIFS with more than 300# of water pressure and a wide fan nozzle from a long way away. Those stains look like they correspond to foam board fasteners. A surface moisture meter will not tell you whats going on at the sheathing depth. A Delmhorst pin type meter is what you need.
That said, I notice the sealant is cracked around the windows, the EIFS doesn’t have a sealant gap there, and the sealant at the roof below has open cracks. A complete EIFS inspection should be called for. IMHO. TG