This question asks whether some verbs are used only with a reflexive pronouns as their object. The accepted answer lists "absent", "avail", "pride", and "content".
If you say "He saw himself in the mirror.", that's plainly not an example, since one can say "He saw the results."
However, besides verbs used only reflexively and at the opposite extreme those like "see", there may be a class of verbs used like this:
He behaved himself.
The crowd at the Trump rally behaved better this time.
They devoted their efforts to winning.
They devoted themselves to only one purpose.
You see that "behave" and "devote" can be used without a reflexive pronoun object. But their uses with such an object are not like "He saw himself in the mirror", where "himself" actually refers to something. Rather, they seem to be phrasal verbs, defined differently and used differently from the ways in which they are defined or used without reflexive object pronouns.
How many reflexive verbs of that kind exist in English?
(There are tons of them in German.)