Might depend on the model year. Friend of mine has/had a fully loaded '69 Imperial coupe, and the headlight washers are activated when the headlights are on, windshield wipers are on and you press the button to squirt the windshield. There is no separate control for them.

Could this be a switch for a rear de-fogger / defroster?

Bloody Mary, Full of Vodka, Blessed art thou among cocktails....