This experiment can only be done at solar noon twice a year; at the spring and autumnal equinox. These are the two times the sun is directly over the equator. You can do this experiment one or two days before or after the equinox to work around cloudy day
This figure-8 path that the sun makes in the sky is called the analemma. On some days you might notice that the sun is not in the sky where, according to the time on your watch, you would expect it to be.