The commercially available solar cookers seem to use a variety of different technologies. I have seen ones that use mirrors, ones that use evacuate tubes, and other things, in different configurations.
I am wondering what combination of solar cooker features would be best at reliably boiling water in dim daylight conditions.
Even evacuated tube designs use focussing mirrors. The mirrors just don't have to be as big or as good. The main benefit of the evacuated tube is in reducing heat loss (just like a vacuum flask) which is very helpful, but only if you have enough of a heat source.
In dim sunlight - (you cast a weak shadow) an evacuated tube would beat a simpler design, but you should increase the size of the mirrors. It would be very slow though. In full sun there's several hundred watts per square metre arriving at the surface (depending on latitude), overcast is more like 100W/m^2 max, dim sunlight somewhere in between. You can't use all of that even if you could focus it. For comparison a domestic electric kettle uses 2000W or more. Immersion heaters designed to run off a car lighter socket and make hot drinks are 120-150W. To get to something close to this power in dim sunlight I'd estimate (perhaps pessimistically) you'd need 2-3 square metres of reflector.
If it's overcast (e.g. you can't see your shadow), you can't focus the light/heat. That's not to say you can't use it at all, but that you can't get a single item particularly hot - forget boiling water. A large array of solar panels would be your best bet there, but they'd need to be massively over-specified as the rated power is in full sunlight. This could power an in-cup water heater or a slow cooker. Of course this would be very expensive.
So for a fixed camp setup, it's not completely impossible if the sun in weak, just very difficult. It is impossible with complete cloud cover.
