The factors which cause the difference between COG and Heading have a greater affect at slow speeds. More importantly, the GPS, which uses historical data to calculate COG, needs a straight line to give an accurate reading. When you make a turn at slow speed, you will need to travel in a straight line for a period of time before the GPS can give you an accurate calculation.
While a boat is at rest, there is no historical data for the GPS. Therefore, there is no COG to report. The COG given by the GPS tends to be erratic and incorrect until you resume movement in a given direction. The Magnetic Compass, however, will give you accurate heading information in real time, from stop to go, and slow to fast.