I have no background in Mechanical Engineering.
It's intuitive to use an analogy as this guy demonstrated here @3:48 where he used caster wheels you would see in office chairs where the contact point is ahead of the wheel in relation to the direction of movement which causes the wheel to trail because of, presumably, the friction of the wheel to the ground resisting the movement which causes the wheel to lag behind which eventually causes it to self-center.
What I don't understand is how is caster wheels in an office chair analogy the same as caster angle describe in the following image and in this video?
In the following image where the wheel is trailing the contact point above it (the rod) seems the exact opposite of the previous image where the the wheel is ahead of the contact point (the suspension).
In an office chair or shopping cart wheel analogy, this is easier to understand as shown in the following illustration.
But as mentioned in @NMech's answer, the above illustrates wheel trailing the input force in the diagram which is different from caster angle shown below.
I am definitely missing something in that diagram I've made. My intuition sees only where the source of input is coming from whether it's behind the wheel or not determines if it's going to resist rotation or turn around. It's hard for me to see how rotational axis being behind the contact patch or not is going to have the same effect.