Yes, they do work on a PWM signal down the yellow or white, sometimes blue wire. It's a 50Hz signal with a pulse width of between 1.0 and 2.0 ms, 1.5ms being the centre of the servo's travel.
Acoms are a well known brand of servo, mainly the lower end of the market. It would seem that they are getting their own chips fab'ed.
I never really bothered taking servo's apart in my RC days, if it was knackered then it was due to mechanical stress. Off road RC racing really hammers even the metal geared high speed, high torque servo's.
If it was a really expensive servo and the output MOSFET's had allowed their smoke to come out then it would be worth mending it, but this was rare.