Lorenjz,
Dunno your background, so forgive me if I start too simple.
Servos all have pots (potentiometers) built into them, driven off the output shaft. They're used to tell the control circuit what angle (roughly) the shaft is pointing, so ohms on the pot can equate to degrees on the servo horn. The control board will spin the motor forward or backward until the pot reads the commanded angle (beyond that, it gets REALLY complicated).
If you replace the built-in pot, and mount it to your camera platform's shaft, the servo control board won't care and will continue to spin the motor until the new pot is pointing at the commanded angle. that way you can change the gearbox to anything you want (like the HEAUGE gear they used), and the servo will still swing left and right proportionally with your stick input.
so what kind of pot do you need? get a good servo, measure the one in it with an ohm meter (measure across all three terminals, in pairs, and pick the highest resistance), and get the same size. Also, make sure you get a linear pot. Audio pots are generally logarithmic, and will give you a funky control.
Let me know if I misunderstood the question.