Is there a reason for the different behaviour of the switch across tools?

yes, GlobalEdgeContinuity is a dialog, not a panel, so it can’t be docked and therefore takes more place in the UI. Therefore collapsing it when not in use.

I could change GEC to a panel, but that would mean I need to revise the UI a bit. I find it currently too wide for conveniently fitting it into a panel compared to other analysis tools.

I don’t know if panels can collapsed this way, but even if there was, I don’t think this is a good idea, since these analysis panels can be docked with other panels.