I have the same machine. It was my first pinball machine and I knew nothing about them. I just needed a project during the first phase of Covid-19. Mine would only turn on all the lights when I first got it. I started at the beginning, trying to figure out why it wouldn't eject a ball to the shooter. Once that was resolved, I just addressed each issue as they became noticeable. When you really get into it, make sure that tic-tac-toe grid in the middle of your playfield is working properly. Each time you score 100 points, the grid should advance to the next number. When you score 500 points, it will advance five numbers. I played mine for six months or so not knowing this. It would only advance when I hit the target at the top of the grid. Once I got the grid to advance properly, it was a completely different game. There's a thread on this, too. It is as simple as adjusting one switch on the 100 point relay located in the back box.
In looking at your photo, I see that you might be missing a nylon nub on the plunger for your middle chime bar. It looks like the chime bar has been rotated due to a hole in it. Here is a thread to the discussion when I had the same issue: https://pinside.com/pinball/forum/topic/williams-chime-bar-failure#post-6125383. You can keep using the chime bar with the hole in it, buy a new one or make a new one. You should replace the plunger, though (or add a nylon tip to yours).
You will have just as much fun fixing/restoring your Gulfstream as playing it. Pinside is such a great forum so you are in the right place. I've always gotten quick replies and suggestions without the snarky comments like on other forums. Make sure your wife is ready to see "Marco Specialties" on your credit card statement and "The Pinball Resource" in your checkbook registry. Both are very reliable suppliers and it is worth every cent to keep them in business.
Have fun.