Apart from the trainers with Baton Pass, and the trainers with high AI, trainers who switch tend to do it at their own dispense. They will just switch when they want to, they don't really have a particular cue that you can activate as the opponent.
As for trainers with high AI like Red in HGSS, for example, he will switch Pokemon in order to get the type advantage on your Pokemon. E.g., if you send out your starter Typhlosion, he will send out Blastoise (if it is usable) as he will then have a type advantage over you and attempt to demolish you. Red is one of the few trainers in any of the main series games that actually has the ability do this.
Hope I helped. :)
