Can himself be (regarded as) an adverb?

From an educational website:

The director of the company wrote to us himself to apologise for the dreadful service.

"himself" goes after a complete verb phrase "wrote to us". Can I regard "himself", similar to "personally" "in person", as a kind of adverb of manner that emphasises the fact that the action of writing is done especially or particularly by the director?

The reasons for my thoughts are as follows:

"himself" is not directly linked with the real subject but comes later. "himself" here doesn't serve as a pronoun to refer to any specific person but to describe/summarise/emphasise a truth. Its function is different from "himself" in "He looked at himself in the mirror", where "himself" really and clearly refers back to a person, the object of a prepositional phrase.

Also from the website

The director of the company himself wrote to us to apologise for the dreadful service.

Here I think "himself" can be a pronoun because it directly goes after the subject. The same person appears twice continuously.

Any ideas about the topic would be appreciated.

"Adverb" is a bit of a catch-all category of words that don't fit into the other word classes. They're words that aren't nouns, verbs, adjectives etc. Words like "very", "again", "however" and "this" are sometimes called adverbs, despite having little syntactic similarity. You can't replace one with another to make a valid sentence.

So, it's possible to regard the emphatic use of reflexive pronouns as acting adverbially; you don't learn much by calling them "adverbs". Most dictionaries don't regard "himself" as an adverb. It is called an "emphatic pronoun" that refers (by anaphora) to a noun or pronoun that has already been used and carries the sense, "and nobody else".

In your example "himself" refers to the director. This anaphora is a function typical of pronouns.

(Etymologyical diversion: Other Germanic languages have a word "self" (or zelf/selv/selbst etc) that can be classed as an "adverb" with meanings like "personally" or "even", and is placed next to nouns and pronouns. But the classification of these words in the Germanic languages is unclear. Some dictionaries call them a "particle", others a "pronoun", and some uses are considered to be "adverb". There are some words that don't neatly fit into the noun/verb/adjective etc categories. The "self" words in Germanic languages are examples of such words.)