Hi
@biggi-up,
I have only driven automatics in the States, on gearboxes without a manual option, so in the absence of other ideas from the forum I've read through the relevant section of my manual (p.131-134) and will interpolate as best I can.
In its usual helpful way, under the heading 'Fault in the automated manual gearbox' (p.133) it says if the car won't move when you select a gear, the system has a fault and you should have it checked (🤦♀️). However, the manual only gets excited if warning lamps are appearing on the dash panel - which doesn't appear to be the situation in your case. As the call-out mechanic (who has actually had a chance to drive/examine the car, unlike us) seems to think it is road-worthy, and the end of July is still a fair ways off, if you are happy to drive it in manual mode you should be ok (though I wouldn't take it for longer jaunts than you're willing to be stranded should it suddenly decide to have a red/orange warning light fault). Something is clearly physically/electronically confused in there if it can pop back into automatic mode when it feels like it, and so the possibility of it refusing to work at all can't be ruled out.
As for when to change gears in manual mode, I will have to assume it works in the same manner as the (fully) manual gearboxes. I would ignore the change up indicator in the dash panel, as this tends to be based more on fuel economy than road conditions, but keep an eye out for the change down indicator, as on mine that's a pretty good sign the road is more inclined than I thought and I need to drop a gear to accommodate it. The general recommendation for small-engined cars like these is to change up around the 2000rpm mark, which is roughly changing up a gear every 10mph when accelerating (so 1st gear up to 10mph, 2nd up to 20mph, 3rd to 30mph, etc.) - although this will obviously depend on the road (hilly roads will see a lot more 2nd gear, for instance). Try to listen to the engine note - if it's high-pitched and/or whining, you're in too low a gear; if it's a low throb (or the car is starting to vibrate/rev needle approaching 1000rpm) you're in too high a gear. If it's purring like a large-ish cat (rev needle somewhere around 14-1500rpm - I haven't looked recently!), you're good to go. Be prepared to drop a gear if you see a hill coming, especially if you're in 5th. Take roundabouts in 2nd if possible.
Hopefully that will keep you moving until the diagnostic test sheds more light on the problem.