I have a '86 300E so I am not sure if this helps, my rear headrests would not fall with the switch. The source of the issue was a disconnected vacuum line going into a rubber connector near the fusebox (under the hood, driver side). I was cleaning out some debris in the area and must have dislodged the connection. All I had to do was push the line back into the junction.

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'86 300E 5 speed
'71 Triumph TR6
'46 Cushman Scooter
'41 Ford 9N tractor