what era are we talking about ?

There are lists of holiday makers published in the Manx press from the turn of the 20th C (giving items such as Mrs Q's boarding house week... - Mr+Mrs A B + family etc. Such lists were common in most seaside towns - if your name is in the paper you tend to buy a copy!

I've never seen lists of passengers off the boats in my use of mid victorian papers nor any reported list of departing passengers (which would have been extremely useful). The number of reported visitors is because of the 1d port tax that had to be colklected (0.5d for under 14's hence the strange half visitors for some years)