Welcome.
+1 for what ponyboy said (BTW - he is a great resource)
I understand your struggle, but in the end it is your car. You should never feel bad doing what you want to it. Being the 2nd owner, there is something said for leaving it original; it is a great story and it you plan to show it in MCA shows, original would be the way to go. But if you plan to just drive and enjoy it, then do what you want to it. My suggestion would be to keep anything you take off. If you ever sell, the next buyer might want it and that would help with resale.
Realize there are many 65's out there, so don't be worried about which path you choose because every combination is out there and some will like what you do and other will not; it is your car, not theirs.
If it helps, I have similar struggles. Mine is a 64 1/2, turns out it is an Arizona car and has all of it original sheet metal (other than I have found some very old fender bender fixes). I feel 'stuck' and have kept it 'original' to what was available in 64. For example, mine did not come with steel style wheels but I like them; since they were a dealer available option I put them on. The same is true with the fog lights, but I was sure to find a factory switch and mount it in the correct location. I also did the accent package minus the paint stripe (i.e. no side 'scoop' molding, add rocker molding).
Things I did that are not 'original': dual exhaust because I like that (although one could argue that a dealer could put them on); changed from blue interior & top to white because I like white much better (changed the data plate to match); rear seat belts because my son was going to ride back there (safety first, and they can be tucked under the seat during shows); mild cam change (no one can see that). And I am in the process of going to a dual master cylinder and relocating the rear brake hose. Even the MCA rules allow for dual master in the driven class, so no harm there.
So (other than probably the white and master cyl) it could have been done back in 64.
Realize, there is no Ford factory documentation for 64-66s saying what they really had, so if you buy one there is no way to know, other than the VIN and data plate items; and you can get repo data plates so that isn't even 100% certain.
And what is my proof that what I did was 'ok'? Years ago (with everything but expect the brake changes), I went to an MCA regional show and took 1st place in the Driven Class. Obviously, I would fail big time in Concourse, but that is not what I care to do.
So where I have been 'stuck' is mods (e.g. disc brakes, fancier wheels/tires, suspension, exterior engine mods, etc.).
So I have done things to my car I like, stayed away from mods, but was able to stay with the MCA rules for 'original'. And in the end, any of that can be reversed if the next owner wants 100% original.
That is the path I chose. And I am not saying you should do that, just pointing out that you can do whatever you want and it is ok.
I hope that helps.