I'm not sure if you're just clutching at straws but if you genuinely think there is a FOV change going on then may I suggest you perhaps visit an optician?
How are my glasses relevant to my maths skills?
Look at the two reference points in the following GIF, made from the same two images. Apart from a slight perspective change (as the exterior camera also shifts from the driving position to centre of the longitudinal axis), the gantry legs and the sign stay pretty much the same size and not too far off the same positions.
However, note that to line up the shots the exterior shot had to be scaled down, effectively pushing it further into the scene (or back in 3D space), like the camera for the exterior shot was, umm, I don't know... further forwards than the cockpit camera.
Cool, so what you proved there is the same thing that my numbers showed: It's a field of view change. Scaling an image is equivalent to zooming, i.e. a field of view change. It's not equivalent to a camera position change. The fact that you could make the images align by scaling one of them proves that it's a field of view change and that the camera did not move along the x axis (forwards).
When a camera moves, the change in apparent object size is not proportional, since objects closer to the camera change size more than objects further away. Thus, you can't make two images align if the camera has changed position.
I never said it feels like the camera is behind the pivot point. Keep trying.
Yes you did:
"Some cars feel like the pivot point is far further than it should be,
like you're driving an extremely fast rear wheel steer forklift truck."
A rear-wheel steer car pivots around the front axle, i.e. you're sitting behind the pivot point.
Edit: Just to illustrate the difference between moving a camera and changing its field of view. Here is a chart where I plotted the difference between moving the camera 1 meter and changing the field of view by -10 degrees. The scaling factor for the apparent size of an object is plotted for various distances. At 1000 meters away, an object's apparent size is barely changing when you move the camera one meter, while at 5 meters the apparent size is almost 25% greater.
At the same time you can see that all objects have their apparent sizes scaled uniformly when you change the field of view, in this case (going from 60 to 50 degrees) they all have a factor of 1.2.
Note that the dotted lines are just there to connect the various data points, the true values would follow a continuous curve.
When you scale an image up or down, you apply a uniform transformation, changing the apparent size of all objects by the same factor, so scaling is equivalent to changing the field of view - not to moving the camera.