'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.

Thingless Nominal Group Embedded As Qualifier

Cf. one too few legs, one too many drinks, one drink too many.

 Woke Alert: May cause offence to unidexters.

Marked Textual Structure Of A Nominal Group

Halliday & Matthiessen (2014: 387, 397):

Textual meaning is embodied throughout the entire structure, since it determines the order in which the elements are arranged, as well as patterns of information structure just as in the clause (note, for example, that the unmarked focus of information in a nominal group is on the word that comes last, not the word that functions as Thing. This means that there is a certain potential for assigning experientially similar meanings different textual statuses within the structure of the nominal group. …

Initial position is thematic; and the natural theme of a process or participant is its relation to the here-and-now. Final position is informative; and the newsworthy component of a process or participant is some aspect of its lexical content. So the structure of groups recapitulates, in the fixed ordering of their elements, the meaning that is incorporated as choice in the message structure of the clause.

Theme Will Tear Us Apart Again

But in Halliday ± Matthiessen (1985, 1994, 2004, 2014), in cases of predicated Theme, the embedded clause is also analysed for Theme:

Decoding And Encoding The Self