There are two stern used
https://www.pinballlife.com/segastern-auto-plunger-arm-weld-assembly.html

Stern machines using plunger and link 515-5338-00:
Striker Xtreme
Sharkey's Shootout
HIgh Roller Casino
Austin Powers
Monopoly
Playboy
RollerCoaster Tycoon
The Simpsons Pinball Party
Terminator 3
The Lord of the Rings
The Lord of the Rings Gold
Ripley's Believe It or Not
Elvis
Elvis Gold
The Sopranos
NASCAR
Grand Prix
World Poker Tour
Pirates of the Caribbean

Stern machines using plunger and link 515-5183-00:
Family Guy
Spider-Man
Black Spider-Man
Wheel of Fortune
Indiana Jones
Batman The Dark Knight
CSI
NBA
24
Iron Man
Big Buck Hunter
Avatar (all models)
Tron (all models)
The Rolling Stones (all models)
Transformers (all models)
AC/DC (all models)
The Avengers (all models)
X-Men (all models)
Metallica (all models)

You will want the 2"
https://www.pinballlife.com/slingshotballshooter-plunger-and-link-2-plunger.html

Excellent observation. I've had 2 break at different locations. I just assumed a worn coil stop where the linkage takes the hit against the coil stop rather than the butt of the plunger. You may be onto something. Go with the 2" as long as it works.

Is there another auto launch used on pirates? I know on BDK there are two.
If the plunger isnt long enough the forks will hit the wood, so depends on application. Makes me think I should check my bdk

Pirates was made in June 2006 which as northvibe pointed out used the 5338 plunger. The very next game released in Feb 2007 used the 5183. I'd bet there was a parts mix up as the parts are almost identical.

Ah! Good catch. I’ve had to double check on our sopranos and BDK as you also never know who did what if they were fixed before you