This is an interesting question - one that is easily answered.
Ever wonder how sightings were taken at sea when there was a heavy overcast or a storm and the sun was NOT visible?
At High Noon, the sun will be at its highest point and no matter how bad the cloud cover is, the sun will ALWAYS be visible at the noon hour, briefly perhaps, slightly dimmed by clouds, but still with enough resolution to make a sighting.
Ask a sailor.
Forget the Mystic Crystal Revelations..
I live in south FL, where it is seldom cloudy all day anyhow, so it may necessarily be awhile before I get a chance to check this out. For the moment, I'm ready to be educated, but am not convinced yet. Very interesting.
The sun will ~sometimes~ be visible through thin clouds and/or fog. But if the cloud cover is very thick at all, the disc of the sun doesn't always come through.
You also need a clear and sharp horizon to do local apparent noon, and weather conditions will foul that up as well.
Sure there are artificial horizon devices, but they're not very reliable. They work, sort of, but aren't to be relied on unless you've got no choice.
The sun will be South of you, when in the Northern hemisphere, your latitude is greater than the suns declination. If you are on the equator and the sun is on the Tropic of Cancer the sun will be to the North.
I have crossed the North Pacific and never saw the sun the entire crossing on numerous crossings. We dead reckoned all the way across. Later we got Sat Nav and then GPS but we still couldn't always see the sun.
Lower latitudes we generally could always get the sun.
Okay, I was a sailor. In fact, my job was navigation. Since you asked, I'll tell you. You have no idea what you're talking about.