Can a captain fly in the right seat as SIC under part 129?
From the regulations:


  Each person acting as a flightcrew member must hold a certificate or
  license that shows the person's ability to perform duties in
  connection with the operation of the aircraft. The certificate or
  license must have been issued or rendered valid by:
  
  (a) The State in which the aircraft is registered; or
  
  (b) The State of the Operator, provided that the State of the Operator
  and the State of Registry have entered into an agreement under Article
  83bis of the Convention on International Civil Aviation that covers
  the aircraft.


Since a captain can always fulfill the duties of a first officer, then yes, someone who normally occupies the left seat can occupy the right seat.