First Analysis:
This is not a mental process, because
(i) himself is not the Phenomenon that he is enjoying;(ii) the unmarked present tense is 'present in present', like behavioural and material clauses.
The clause is agnate with he is enjoying [[what he is doing]],
so himself serves the same function as the Behaviour what he is doing.
Here 'enjoy' adds an emotional feature to a behavioural Process.
Final Analysis:
In the case of this reflexive verb, the Range of the Process is better analysed as included in the Process itself (like behaving himself):
Of the two-participant process types, behavioural is the only that excludes the possibility of a reflexive pronoun, since the second participant is limited to a behaviour. For example,
- material: he cut himself
- mental: he saw himself
- verbal: he flattered himself
- relational: he wasn't himself
So wordings like 'enjoy oneself' and 'behave oneself' must function as a behavioural Process.
