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You could use a utility knife. You'd have to make numerous progressively-deeper cuts, but you'd end up with a cleaner edge. If you do use a jigsaw, make sure you have a sharp and narrow blade so it doesn't chew up the edge too much. Another option would be to install an access door (if it isn't a conspicuous spot). Home stores sell plastic plumbing access doors that are designed to fit between two studs. That would mean you wouldn't have to try to reuse the drywall or worry too much about a smooth edge, and of course any future repairs would be much easier.
An amatuer advise Design a chasis first(choose a series DCmotor which work with the power available from battery) give provision for motor and battery, others will just fit in I guess Connect the motor circuit with switch between motor and battery Use two rubber rollers to grip the string, one being driven by motor with a suitable ratioed gear(it will depend upon the weight of setup) or a belt drive(will be easier to make, further you can give provision to vary the ratio) Fix the snap connector. The series motor can give enough for the starting torque. Try to roll on
