Latitude can only be determined at local noon, with instruments that are not practical to use at sea.

They had a floating sundial disc that was used to tell local time. You plop it in a bucket and it stays upright.

Before you set sail, you observe how tall the shadows get in your sundial and use that as a reference point. Then at sea, you keep watch whether the noon shadow is shorter or taller than what you had at home, and you know whether you've drifted off your intended latitude.

When it's cloudy and you don't have a shadow, you just try your best to keep your heading by using the sunstone, because you still know approximately what time it is from how high the sun is, and even if you didn't, keeping the sun at a fixed angle to your boat will keep you heading the same way on average.

No need to wait for singularities, like a solstice or equinox

Can't see the pole star during the day, so you have to tell direction by the sun.

The reason to sail at the equinox is because the day and night are equal time, so the sun rises directly from the east and sets exactly in the west - helps a great deal.

On the summer solstice in the north, the day is almost 24 hours long and the sun just barely dips down in the north - again a very useful clue as to where you're going, and also safer because there's no "moonstone" to see the Pole Star through clouds. The longer you have daylight, the safer.

You don't want to sail in the autumn because you'll get stuck over there for the winter without knowing whether you have anything to eat or live by, and you don't want to sail in the winter because it's freezing cold and the weather is bad. Hence, most of the sailing was done in early spring, summer, and the return trip was scheduled for late summer.

But for contemporary generation of nerds experienced with computers but separated from reality is way more comfortable to make simulations ad nauseam rather than really test something experimentally.

The power of computer simulations is that you can make monte carlo simulations, where you introduce random errors in the navigator's efforts and run thousands and thousands of variations of the trip to see where it would end up. If the navigation method is accurate enough, the probability of ending up in the right place is maintained despite the small errors. If not, the errors compound and most of the ships get lost.

Making the real experiment would result only in anecdotal evidence, as one trip across the ocean can't tell whether you got there by skill or by luck, and making hundreds of voyages would be infeasible, and also irrelevant as the navigators would be complete amateurs compared to their Viking counterparts who did much more than just gaze at the sun.

the computer simulations are one thing and experiments in field another one

The point of the simulation was to first perform the field experiments to find the limits and range of accuracy to expect out of a sunstone as a navigation system, and then plug these limits into the virtual model to constrain the virtual navigator, and then find out whether that level of accuracy would be enough to reach the destination.

most of really useful inventions and findings has been found accidentally

Here the "accidentally" part of discovery was eliminated by randomizing enough journeys so what would have been found by accident became inevitable. A real expedition would not have been able to measure the effect of periodicity/symmetry if they were following viking habits, since they wouldn't have had a clock on the boat.

The Vikings, like all seafarers in the northern hemisphere, could determine their latitude by measuring the Pole Star's angular distance above the horizon: any season, all night long. No need to wait for singularities, like a solstice or equinox.

The thing is: a sunstone works even in cloudy weather. Looking at the Pole star doesn't.