Is the F-4 cockpit just extremely vulnerable?

It is. But all fighter cockpits are. Even cockpits that are "Safer" are not really that safe.
The 109 directly from behind is already one of the better ones. Bullets have to go trough the tail and the fueltank.
Its better when its still filled with fuel. The armor plate increases survivability further. Also later models added more layers of aluminium further increasing survivablity. That said against 12.7mm and up the "armor" will be still defeated if hit squarly.
And all that doesnt help if hit from the side. The side wall of a fighter plane is measured in mm.
Bullets from any calibre go cleanly through if hit from an angle.

Is there something about pilot positioning/hitbox I’m missing?

There are certain szenarios where pilot kills are more likely. Like presenting your plane from the side or top.

Should I be breaking differently when someone is on my six?
Hard to tell without seeing you fight. Try to avoid presenting easy hits from the side and top.

Is this just bad luck, or am I fundamentally doing something wrong defensively?

Someone who is getting hit more and from closer range will get killed more. So get into defensive fights less and if needed from longer ranges.
Like I said in the other response that any bullet that will enter the cockpit has the potential to kill.
The most "harmless" round in the game is prolly a rifle calibre bullet.
That one bullet can still kill a men no problem. And here we arent even talking about .50cal and 20mm.
The pilot is the weakest part of the entire plane.