Wikipedia's article on the building gives the story in a sentence: the house is said to be haunted, soldiers saw a face come through a wall, and the face may be the ghost of the 9th Earl of Argyll. The building was owned by the Dukes of Argyll until 1769 and later used as a military hospital, which is likely the setting for the soldiers' sighting, though no date is given.
The attribution to the earl is a suggestion, not something the witnesses said. He had led a rising against James VII and was executed in Edinburgh, not at Stirling. This is a very short traditional tale with no first-hand account.
Comments