If I'm not wrong, the PTU runs for a bit during the 2nd engine start for testing purposes. So that should cover the first escenario you heard it in. As for why it was running during taxi out with both engines, beats me! I've heard it run during SINGLE engine taxi when the crew forgets to run the Y elec pump, but that's about it.
I´ve heard it go at gear up and down too, but never payed too much interest to it, so I don't have an answer for that either. But yours sounds logical. Though I think the drop is not for enough time to trigger the PTU?