[By.Jove (Jove)]

Surely a plumbob - piece of string with a pointy weight at the bottom - would be better than relying on any level to get a true vertical gnomon ? Then it doesn't matter whether the ground is not level, or uneven. If you need to damp it so doesn't swing in a breeze, place a dish of cooking oil or fine sand under the plumbob so the tip drags in it. Even a rock on a piece of string would do.

There's another method I've used which is useful in summer when shadows are very short around noon. Choose times a couple of hours either side of solar noon eg. solar noon - 2h and solar noon + 2h, and at the appointed times, trace the shadow cast by the vertical. Using school geometry, bisect the angle between these lines to find south. You can repeat this at hourly intervals as well, eg +/- 1h, +/-2h, +/-3h which then gives several measurements over a day.