An interesting tale and worthy of investigation, as usual, conflicting accounts when googled. Some say Humphrey Barton's book, Atlantic Adventures, gives the best account, so might be worth a read if you haven't already done so. There are many different thoughts on where they came from and country of birth.Buckley, could have been Irish or American and Primoraz, Australian or Croatian. However, if Primoraz was here in an asylum in 1881 it should show on the 1881 census, it doesn't or any of his other names he may of used.
Strangely, there is a registered death in 1886
Nicola Primoraz, age 43
Volume 8b Page 561,
It doesn't say whether its male or female, you could obtain the death certificate from the GRO office, but it will cost you close to £10,
Prescot was the registration district for Rainhill Asylum.
The dogs name was Boatswain, no info on him.