A cam switch assembly is actuated by movement of a member, such as a part of a convertible top that is pivoted about a first pivot axis toward and away from a surface that is fixed relative to the pivot. The cam switch comprises a holder for at least one switch that is attached to the member. A cam switch actuator having an arm is attached to the holder at a second pivot axis. The cam switch actuator opens and closes the switch as the cam switch actuator is pivoted relative to the holder about the second pivot axis. The arm has a first lost motion connection to the movable member in a first direction. The member has a second lost motion connection at the first pivot axis that is aligned with the first direction when the member is moved into engagement with the surface. The member is movable relative to the surface in a first direction and the arm is permitted to move relative to the surface without changing the angular orientation of the cam switch actuator relative to the holder.