I'm not familiar with the Trendscout, but the usual procedure for an airlock is to suck through the tap with it turned on (using a bit of flexible tube if necessary) until water flows through. Not sure why it should work when the washroom tap is on though. If it's a pressure-operated system that might have something to do with it.
Basically, there are two kinds of pump operating system. Pressure ones switch the pump on whenever the pressure drops (by a tap being open). Microswitch ones are switched on directly when the tap is turned - you can identify these by the fact that there are two wires connected to the underside of the tap - pressure ones have no wiring anywhere near the tap, it's all at the pump.