Well, weelitttledrummer, Liverpool does come into it.

"When I was a youngster, I sailed with the best
On a Liverpool packet bound out for the west."

The ship then calls in at Cork (or Queenstown - Cobh).

"We sheltered one day in the harbour of Cork
And then we set out for the port of New York."

Since no ship sailed non-stop from Liverpool to San Francisco, this ship was enroute to San Francisco via Queenstown and New York and, likely, a few other places in South America. But our hero was enticed off his ship in New York by a job. When the New York boarding house master got a call for sailors from another ship, our hero was doped and wound up in rough shape, penniless and headed around Cape Horn.

I assume everyone knows Stan Hugill included this in Shanties from the Seven Seas. He said his version came from an Irish sailing ship mariner, Paddy Delaney. This song appeared in collections beginning about 1915.

All the best,
Dan