An accommodating contact lens comprises a control device, which comprises one or more eyelid engagement structures. The eyelid engagement structures are configured to move with the eyelid relative to the contact lens. The eyelid engagement structure is coupled to the eyelid and to the accommodating contact lens, which may comprise a fluidic module having inner and outer fluid reservoirs. The eyelid engagement structure is configured to respond to the narrowing or widening of the eyelid fissure, moving a fluid in or out of the inner reservoir to accommodate near or far vision.