That's a terrible way of doing it, for several reasons.
Firstly, unlike a microcontroller, the Pi doesn't have a hardware PWM output, so driving servos directly from the GPIO is asking for trouble (bit-banging will result in high CPU use and glitchy output). The voltage would be wrong, too, so you'd need some level-conversion electronics.
https://www.adafruit.com/products/815 is a good way to interface them. I've used it and it Just Works. You just write the magic numbers to the I
2C device.
Once that's taken care of, driving a mechanical dimmer switch with a servo is, well, daft.
If it has to be a mains lamp, get a dimmer that can be controlled electronically. 0-10V analogue used to be the thing (DAC left as an exercise for the reader - a resistor network might suffice), but I'm sure that someone must make small dimmers with a more friendly serial interface than DMX512.
Or use a low-voltage lamp and control it electronically - PWM some LEDs with a MOSFET (or better, a dimmable constant-current LED driver) or something. Or use some of those addressable RGB LED strips - then all the Pi has to do is tell them what colour to be. I did a surprisingly good sunrise/set effect on one of those for a project that YACFers may have heard about.
...but if you insist, servos tend to be specified by the amount of torque available (amongst other things), so a bit of year 9 physics to determine the amount needed to click the switch would be where I'd start, unless I had some servos to hand to suck and see.
The other thing about servos is they tend to be a bit twitchy when at rest. That could translate to annoying flicker, especially if the dimmer pot is less than smooth. A stepper motor would avoid that, but they need more complex drive electronics, and you'll need a strategy for finding the home position on start-up, even if it's just headbanging the end of travel inna 1541 stylee. Torquey stepper motors aren't cheap. You might find one in a printer or something.