This surgery is technically quite elaborate and requires a good team approach and a close and personal contact with the patient. You should make sure that 1) the center of your choice has ample experience in this field 2) the team managing your father is readily available and offeres 24/7 coverage 3) there is a movement disorder patient group available that has experience with this , which may provide a good resource to you.
The surgical aspect is considered "low risk" if done well, and carries the ususal risk of brain surgery (infection/bleeding/wound healing
difficulties/fluid leak) and in rare cases also strokes or anesthesia
related problems. The device works well for several years, until the pulse generator battery needs to be changed.
Complication rates correlate to the volume and experience of the surgical team, and you should ask about this locally - but do not be afraid, it is considered a rather safe surgery, when done well.