To explain the schematic:
R1, R2 & R3 are variable resistors, to allow fine tuning of the system.
C1 is a capacitor
B1 is a double-pole, single throw, momentary pushbutton
M1 is the DC motor

When button B1 is pressed, motor M1 runs forward for 5xC1x(R1+R3) seconds.

When button B1 is released, motor M1 runs backwards for 5xC1x(R2+R3) seconds

R1 controls the eye close speed
R2 controls the eye open speed
R3 is the master speed control

C1 & R3 are crucial for controlling cycle lengthC1 will need to be selected so that 5xC1XR3 seconds matches with one half cycle of the gearwork (Eye open to eye closed)