From a controller's perspective I would consider - and it is the assumption I made with my earlier post - a swing-over (or any similar manoeuvre) to be circling after an instrument approach. That is to say, the change to another landing runway is made visually and not a change to the ILS etc. nominated by ATC (in the latter case I would consider it to be an instrument approach to that other runway with the associated missed approach flown if it is necessary). The fact that certain aircraft operators have internal SOPs or flight profile monitoring systems that prevent pilots from accepting the manoeuvre is irrelevant to the main question here.
Reference to ICAO PANS-OPS (although I must admit that I'm not certain that it is the latest edition) includes the statement
Visual manoeuvring (circling) is the term used to describe the phase of flight after an instrument approach has been completed. It brings the aircraft into position for landing on a runway which is not suitably located for straight-in approach, i.e. one where the criteria for alignment or descent gradient cannot be met.
This does not strictly describe a swing-over but it is the closest I can find. If one accepts that a swing-over is circling, then the definitive answer seems to be given by PANS-OPS - reproduced below:
MISSED APPROACH PROCEDURE WHILE CIRCLING
If visual reference is lost while circling to land from an instrument approach, the missed approach specified for that particular procedure must be followed. The pilot will make an initial climbing turn toward the landing runway and overhead the aerodrome. At this point, the pilot will establish the aircraft climbing on the missed approach track.
The circling manoeuvre may he carried out in more than one direction. For this reason, different patterns are required to establish the aircraft on the prescribed missed approach course depending on its position at the time visual reference is lost.
If, on the other hand, one does not accept a swing-over to be circling after an instrument approach, please disregard all the above!