Anyway, the exterior stucco seems to have gone rotten from a combination of moisture wicking up from the earth via the stucco that had been spread down into the soil line (a total no-no) and the moisture inside the walls from the leaking shower pan way back when. That internal leak had no doubt been going for some years, and the stucco-in-the-ground was 50 years old, so rotten is no surprise.
As a result we've had the stucco subcontractors strip most of the exterior of the gable end off. This has given us an opportunity to add insulation in the wall - we had none before, which makes the way our room got very cold in the winter more understandable - and there will be a new moisture barrier under the sheathing. An unexpected but appropriate upgrade.