You can make a windshield wiper motor work or a washing machine motor work or a whole lot of other electrical motors work. The trick is how much is it going to cost you and knowing how to do it. Most likely the windshield wiper motor will turn to fast as it comes straight out of a car. You will need some sort of PluseWidth Modulator (PWM) to slow down the speed, and their are plenty of plans on the internet to show you how to build your own PWM. You might be able to get by with a dimmer switch, but reduceing the voltage might burn up the motor and could cause excessive heat buildup. My biggest concern is the bulk in the size of a wiper motor. The sheer size of the wipermotor will mean making a pretty big cabinet just to house the motor. Also the wiper motor most likely will be 12V DC which would mean some sort of inverter to convert the AC house power to DC voltages.
I have already been there, done that, using wiper motors, retractable electric radio antennas, BBQ rottessories, and a bunch of other things. Yea, you can do it, but makeing it work like you want it too isnt always easy. I'm not trying to be negative, but sometimes its better to go ahead and bite the bullet and buy something you know works, than waste a bunch of time and money only to endup having to scrap it and start over.
The little motor in my pic's cost $12, its a low voltage gear motor and I know from experience it will turn three trays holding 288 eggs. Chris can sell you the controller for not much more than the cost of of the motor. You will have to make the wiper style connecting arm, but if you can make a wiper motor work, you can figure how to make the arm and mount it on the little gear motor. All you need is a drill and a drill bit.