Reflexive verbs

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.)

I cannot quantify (and I find it hard to imagine how to, anyway) and I think there will be some debatable cases (as your second example, devote, exemplifies).

This short entry, apart from giving interesting examples, points out that the presence of a reflexive pronoun is not necessary for a verb to qualify as reflexive. They kissed is a reflexive usage (reciprocal). It also points out behave as an intransitive verb that nevertheless admits a reflexive pronoun, as in your example.

It further gives a list of verbs that change their meaning when a reflexive pronoun takes the role of the object. I guess there will be quite a list of these.

You forget yourself

arguably means something quite different from you forget John, in that you do not really forget the object. Similarly: enjoy oneself, embarass oneself, repeat oneself, etc.

This post introduces identify as arguably reflexive (intransitive) verb. Interestingly, the entry linked earlier also qualifies laugh (as in "They laughed.") as purely reflexive; I find this peculiar, even though the verb happens to translate as reflexive in my own language.