After trying out a weak DC motor to no avail, I rigged up a continuous drive servo motor to try to open a curtain.

I started off by supergluing an old curtain rod holder to a servo. This guides the string onto the spool and makes for much smoother operation. Below you can see the gluing process and the first test of the Servo motor with the spool:

I wrote some basic Arduino code to turn the servo forwards/backwards using two buttons. You can check out the commit here: https://github.com/jerwil/Automated_Curtains/commit/0a2c84b8c485c43f2e53a2dcb1959fb2c830cd2b