This article is from the Final-Fantasy and other Square Soft Games FAQ, by email@example.com (Nick Zitzmann) with numerous contributions by others.
After choosing to dig for the Lunar Harp, try putting excavators at the
four compass points of the digging area. Then watch in what direction
they turn their heads--this will clue you in to the Harp's location.
Give up? Go to the upper level of the digging area. Move _slightly_
south from the left edge of the tent and move a little ways to the west.
Dig, and you'll get the Lunar Harp the next morning.