I came up with a plan for a light dep controller that shouldn't cost more than $250 to make. At home I use a Vera Zwave controller to run house lights, grow room, hydroponic pumps, measuring 10 gallon increments ect. Zwave is a wireless remote control setup. A cheap Vera lite controller can be had for $60. Appliance 15 amp modules and dual 10 amp plug in modules are about $30. Vera can do simple on-off commands, dimming, or commands based on a time schedule, including sunrise, sunset. Vera can also do 'Scenes' where sequences or macros can be easily built to do sequential, scheduled, or if-then commands. All of this cam be overseen or operated from a cell phone or computer.
For the controller, two pairs of wires come in, one pair each motor. They get joined green to green and red to red. the power comes from four 12v automotive type solenoids(1, 2, 3, 4) powered by transformers connected to the Zwave modules. The joined red and green wires go to the solenoids. Red goes to 1 and 3. Green goes to 2 and 4. With 4 zwave modules, scenes can be created to power the solenoids reversing the polarity of the power to the motors. A little tinkering would give the exact amount of time for the extension and retraction of the light dep tarp. The tarp motors can be run from a battery.