Took it for another test spin this morning. It's been relatively dry for the past two days and I've been hoping that if my problem was dampness related that it might dry out.
As usual, within 2-3 minutes after starting the car, the stream of water from the washers resumed. Playing with the wash/wipe switch revealed that pulling it toward me and holding it would actually STOP the washers, contrary to its normal operation. The wipers themselves worked as they should. Once I released the switch the stream of water (i got tired of putting fluid in there) resumed. Once or twice the flood quit and the washers functioned normally, i.e. only when activated (!).
This disposes me to favor the switch diagnosis. If this were a short down the line I would think that the switch position would have no effect, but I may be wrong. I have not tried disconnecting the multi function altogether but may do so later today.