Idling rough, clicking when using heat

When idling, it produces a rhythmic popping feeling and sound in the center of the vehicle, one that feels almost like it is originating from the drive-train. However, the vehicle does not have issues with stalling, and the feeling is not present while driving at higher speeds. It also does not sound or feel like it comes from the engine block. Does anyone have any idea what this might be?

Additionally, after turning on the heat/defroster, there is a periodic clicking sound that comes from what sounds like the engine block, as opposed to the dashboard. The heat also works, which leads me to believe that it is not the actuator that some Windstar owners have had issues with. Does anyone have any idea what this could be?