I haven't done this quest in a long time, but I know some of the timers on this server go in increments of 6, 12, or even 24 (or more) hours. The pirate items are decently powered, so I would expect at least one pirate to have a long timer on him. I like to leave my character afk in areas, hidden of course, and check my journal periodically to see if anything has happened. You'd be surprised at how well these players have these timers clocked. They'll figure out the respawn timer and as soon as it spawns they'll be there within minutes.
One of my favorite things to do is reveal hidden players, or find the recall spot of the camping veteran, and then block it. Some of these people don't have real lives outside of Ultima, and due to that have an advantage over you. Trolling them is one of those small comforts.
If you do manage to kill the pirate before they show up, make sure to grab the corpse. That way when they get there they'll be waiting for nothing. I know this sounds mean spirited, but its actually not. There is no reason whatsoever that a single player should have a specific item or quest locked down to the point that no one else can do them. It detracts from the game, the economy, and the experience of everyone. So have fun and get creative.
Just make sure that you don't become that guy in the process.