A sink without a fresh water tank doesn't make much sense so I'm inclined to say they have a tank.
I found some photos of a 1996 Jayco 1006 online and it appears that the fresh water fill port is high on the left (driver's) side, above the water heater access door, and just in front of the wheel. It will be a white cap about 2" diameter. The city water inlet appears to be next to the tank fill (garden hose connection). Most popups do not fill the tank from the city water inlet like many/most larger rigs.
The electric water pump will need to be turned on. There is probably a small switch near the galley for that.
The electric water pump will most likely be powered through the galley kill switch. Do the overhead lights work AND is the pump switch on? If so, then the kill switch is engaged. This kill switch is the source and solution for many 12Vdc problems! Mine's pretty picky; the galley has to be set in place just right. The overhead lights are the key indicator in this case; they are powered through the kill switch too.
Now check the fuse in the 12Vdc distribution panel. My unit has the 12Vdc fuses in the same access panel as the 120Vac circuit breakers (and the converter is in there too!). While they are looking there, have them check all the fuses. Just pull them out one at a time and look to see if the fuse element is solid. Flip the breakers off & on to excercise them (do this once a year; both in the RV and in the sticks & bricks).
Now assuming the kill switch is properly engaged, pump switch is on, the fuses are good, and it STILL doesn't work, check for an in-line fuse near the water pump. The pump could be almost anywhere inside the trailer, but start looking near the water heater. They may have to remove some seat cushions or open cabinet doors to find it. It will be a cylinder about 10" high and 4" diameter with wires and pipes going to it. The in-line fuse is probably within 6-12" of the pump.
Now if everything above checks out OK, and the pump STILL doesn't work, they need to determine if the pump works. Have them open the faucet valves (to engage the low-pressure switch) and check voltage at the in-line fuse. If the meter reads 12Vdc (or more) at this point, the pump is probably shot and needs replaced.
Good luck to them!
2004 Toyota Tundra SR5 (V8, 4WD, TP, TRD)
2005 Fleetwod Allegance with axle flip
Honeywell 2000i Generator
Me, DW, DS, DD, & Chicken-Dog