It appears it's a Model 1003 from 1980. I will contact them to ask where to find pieces. Is the website trustworthy? It looks like it hasn't been updated since the mid 90s.
Thank you for your help!
I don't think you should confuse the fact that there aren't any models after the mid-90s with the site not having been updates. The Targa hasn't been produced by Sheaffer since the 90's.
Have you unscrewed the barrel and had a look inside? Quite possibly there's a cartridge or converter inside. If so, pull it out and pop the nib section into some cool water to soak. If ink runs out into the water, keep soaking in changes of fresh water till no more comes out. A gentle blow (after most of the dried ink is gone...) through the open end will help clear things.
If there's a converter ( likely a stainless tube with a rubber sac inside and a press bar ) then clean that out as well by filling and flushing with water. It's possible the rubber may have perished, but I have several of these and all are still going strong after 30+ years. If it's a cartridge, any standard Sheaffer cartridge will fit, or you can flush and re-fill the one you have with ink - make sure it's designed specifically for fountain pens - and a blunt needle syringe.
Good luck - these are great pens.