Determining South (in the Northern hemisphere) from a clock
Hmm, I wonder if there is an app for that? Point arrow on screen in heading of the sun, and in combination with (GPS or other time source) time, get second arrow pointing due South (in Northern hemisphere), and due North (in Southern hemisphere). GPS or external knowledge could be used to work out which hemisphere you are in.
Note: GPS (with a single antenna) will not tell you which way is North. It determines your position on the geoid only, not heading. You need two points, either by having two antennas, or by moving and taking a second reading before GPS can then calculate and tell you which direction is North relative to the course between the points. Hence the need for a compass of some type (magnetic/gyro/inertial) in combination with GPS for some applications.
Of course, many smartphones have magnetometers in them that can be used to emulate a magnetic compass.
One of my prize possessions is a 24-hour dial wristwatch with mid-day at the top of the dial, which allows you to determine South (in the Northern hemisphere) directly (point hour-hand at sun, mid-day marker points due South). The irritation is that the mid-night marker is labelled 24, rather than 0.