I don't know how GoNorthEast manage at Hexham for driver rest periods, but they seem to keep a Ten available to slot-in whenever the incoming bus is running late (even by a couple of minutes - I've seen the incoming vehicle entering the bus station as the 'float' vehicle is driven onto the departure stand).
Of course it is the driver, not the vehicle that is due the rest period, but, maybe they have a spare driver too? - though there is a nine-minute 'layover' between arrival and departure in addition to the 30 minute gap.

The X84/X85 only has a 5 minute 'layover' between journeys in Hexham and 8 minutes in Newcastle (I don't think the driver changes in Newcastle) - but the X84/X85 alternate at each end of the route (ie change the destination blind).
I've never seen a spare X84/X85 vehicle parked-up in Hexham (though perhaps they could fetch one from the depot if the incoming was seriously late?)

The 687 has a 30 minute 'gap' between arrival and departure from Hexham bus station (with a trip to Hexham (Priestlands) during that 30 minutes. Drivers do more than one round-trip to Corbridge before changing over.