Hmm... This is an odd one indeed. If a guitar tech can't find the problem with the instrument on his workbench, what hope have we..? That being said, there are many potential, albeit rare, reasons for no, or little, volume. The jack socket has been eliminated, but, as we go deeper into the signal chain, we could suspect an issue with the internal wiring, a badly-soldered joint to the potentiometers, a faulty component (tone capacitor..?), dust, dirt or worse in the volume pots, duff contacts on the selector switch and, lastly but least likely, both pick-ups having broken or shorted coil windings. These guitars are not rocket surgery, but are slightly more difficult to work on, as access to the cabling etc is poor. However, any decent guitar tech should be able to at least determine the cause, with a few fairly basic tests. I'd recommend going to another technician for a second opinion; to me, the best 'guess' would be the selector switch being stuck. Hope this helps.