'Enjoy Oneself' As Behavioural Process

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.