My husband has Parkinsons and constipation is a part of the disease. The natural wave action of the bowel is not being triggered by the neurological impulses as it is in you and me.
We have found that maganesium oxide or Epsom Salts taken at night before bedtime is the path to more normal bowel movements.

Maintainence dose would be approx. 1/2 to one teaspoon.

Also be sure that he drinks at least 8 big BIG glasses of pure water every 24 hour period. Constipation is in part dehydration, and anything that adds to the burden with a Parkinsons victim is too much.
The toxins build up in the body and brain and the ability to function drops off badly when the bowels do not move AT LEAST once a day. Preferably 3 times a day to keep the mind as clear as possible.

You have my sympathy. This is a terrible disease to have or to care for.

Nancy