Much of Guernsey was used for horticulture and was covered in glass at the time.
Sgt Stirling's story has been put together by island guide Tim Osborne who heard about it from a member of the family that hid him overnight.
Tim said: "Somewhere he lost his bearing. He then saw a flick of light that he thought was the White Cliffs of Dover. But these were actually greenhouses in Guernsey. He was almost out of fuel and opted to bail out and was lucky to land in one piece on Lihou Island near Guernsey.
"He managed to bury his parachute and dust himself down before walking across the causeway [to Guernsey] and a minefield without knowing it.