Not sure which book
I just happened to glance thru it at the main reference library while waiting to look at some photos
I have no idea where it is, but there is always talk about smugglers on the gulley that leads up to The Dungeon, there is also mention of a smuuglers cave in Thurstaston Village, whether that is tied to the tunnel that was found or independent I don't know.
When the Wirral Tour Bus included a Smugglers Cave on it's tour around the Heswall area in 2005, it *implied* that access to the cave is normally restricted ie it is on private property.
I think there is a bit of a cave on heswall dales but is about as exciting as The Dungeon.
Many Smugglers Caves around the country turn out to just be little nooks and crannies that Smugglers may have used to hide stuff - not on your tunnel scale. Red Rocks springs to mine as being similar in stature to some I have seen.