Thanks Jim! Good video, but oddly enough, the Chevelle and GTO are much different in this regard. The Chevelle has the plastic square piece that seems to completely fill the hole. Then the screw goes in and it seems more stable than what I have. Mine do not completely fill the hole and they wobble about more. I am sure this allows them to lean over and come out of the bucket more. I wonder if that is what the GTO is supposed to have and when my car was restored, they used a GM headlight retaining and adjustment screw, but not one for the A body. I have the chassis manual for my car, but in some ways it is poor. In this case, I found nothing on headlight positioning, screws and buckets (unless is in a section I didn't see). Also different is on the Chevelle, the spring attaches on the back. On the GTO, the spring comes up and over the edge of the bucket.
I attached a few more pictures 1) A close up of my installed adjustment screw - but you cannot really tell how it wobbles like I mentioned. Pictures 2 and 3 are of the adjustment screw not installed.
I have not found anything like that Chevelle video for the GTO that would allow me to validate if I am supposed to have the Chevelle setup. If bending the tabs of the bucket (as mentioned earlier) does not work, I may try the Chevelle set up.
The only diagram I could find is not very revealing.
I see you have the small spring at the lower corner of the bucket in your photo, but I have included 2 pics off Ebay for the 1968-69 headlight panel and you will see the spring at the bottom corner which hooks into the recess on the bucket at the bottom corner - like you have, so that appears to be correct. You can also see the nylon/plastic attachment points and screw. I also included a 1970 headlight panel. You can see all of them have the "pocket" where the spring fits and the OPGI spring listed below should be this type used in the pockets.
Those adjusters may not be correct. They might simply be the Dorman replacement type you find at auto parts stores.
Here is what OPGI has to offer - says it will fit 1969: https://www.opgi.com/gto/G240842/
Now if you look at the Chevelle offering, looks to be the same adjusters, different springs - which may be due to the earlier design to hold the headlights in using the headlight ring (see the 1967 Lemans video): https://www.opgi.com/chevelle/CH4055/
Here is the correct bucket springs for your application: https://www.opgi.com/gto/G241117/
I included a photo of the stainless ring that goes over the headlight and screws to those 3 small round holes on the outer edge of your bucket. I was mistaken
in my first post thinking the spring was attached to that hole. However, it just seems to stick in my mind that there was a spring that went from the stainless ring to the headlight panel and it was a real pain to fight. The picture shows an "oval slot" just below the attachment screw and I am thinking that this is where that spring may have gone - but I have not done the old T-3 headlight replacement in quite some time.
So I might try a new/different style of nylon clips from OPGI to see if they fit tighter and don't flop around. This may be a good part of the problem.
Also found another video on YouTube. It is a 1967 Lemans, but it shows 2 things. What is needed to fit the replacement headlights (which I assume are not the old T3, but store bought replacements) and the fight with the spring on the headlight ring starting at minute 4:32. But, this may not apply to the '69 headlights as they may have been redesigned and the spring in the lower side may have been an upgrade to what I remember fighting.
Here is another YouTube that shows a headlight/bucket installation that looks more like yours. You attachment spring is slightly different in that it does not clip into the hole in the bucket. So may be of some help.