I'm pretty certain I remember correctly about when the tunnel was made. Phillipos at the Meltemi was my first source. I know the story was confirmed in some travel-guide later on, but I can't remember which one. Maybe someone down there could find somebody who has been there the last 60 years and ask them.
Another thought just appeared: Wouldn't all supplies to anywhere on the south coast have to be brought in by boat anyway?
You are the war historian, Chris, so I expect you'll come up with the correct story soon.
Back in the 80s the tunnels were used as shelter by sheep trying to escape the sun, at day time, and by shoestring travelers trying to escape both the rain and the cost of a hostel bed, at night time. Both daytime and nighttime occupiers left stuff on the ground, so trying to get through the first tunnel without a torch was quite adventurous.