do you mean you need to trigger a function that's not a new turn?
how about using UnitSelectionChanged or SerialEventUnitMove?
or one of the other unit themed GameEvents, seeing as that's probably something that should get triggered during the human player's turn
you could also use one of the city events like SerialEventCityScreenDirty or SerialEventCityInfoDirty (but I don't know exactly when those fire)