Shadow clocks were used to find longitude in both the East and West thousands of years ago, but the knowledge was lost (like most things known and in common use in the Classical Christian Era by the hundred years war (628-723AD) by the Varsity muslim armies led by Mohammad and his successors, who destroyed everything that was not in the koran - even to creating the desert conditions in today’s north Africa using vast goat herds to eat the vegetation).
I can see how you would use a shadow to calculate latitude, but how would it be used for longitude? Everywhere on the same latitude has the same path of the sun’s shadow during a day. The fraction of a degree change in the sun’s position from one day to the next would have been too small to detect.