'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.

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:

Targeting Authority On One's Own Behalf

Non-Behavioural Laughing

Direction Of Coding And Agency

A decoding identifying clause can be middle or effective:

but an encoding identifying clause is always effective:

Decoding vs Encoding Interrogatives

'Show' As Material Process Embedded In Encoding Relational Clause

The verb show also serves as a relational or verbal Process.

Blowin' In The Wind

Role As Identifier Value

Clause-Final Subject

Adverbial Group Of Cause Serving As Verbiage And Phenomenon Participants

The "Agency" Of Genes

The Existence Of Words

'Be' As Material Process

'Lead' As Circumstantial Identifying Process

Attribute As Unmarked Theme

Identifying Clause Without Medium (Identified Token)

Descartes' Reification Of Sensing

An Enclosed Structurally Unrelated Clause

Mr Minter, 'Call me Ted', was  a large, untidy, perpetually smiling man with the look of an astute rabbit.

— John Mortimer Rumpole And The Asylum Seekers

One way to analyse the enclosed clause as structurally related is to take the view from below. Because it is realised as its own tone group (TONALITY) and realised by tone concord with what precedes (TONE), the enclosed clause is realised as if it were in non-defining elaborating relationship with the surrounding clause. Such an interpretation, though, requires treating the clause that projected it as ellipsed.

Intense Emotion Without Graduated Affect

This is an experiential construal of intense emotion but not an interpersonal enactment of graduated affect. This is because AFFECT is the system of enacting a positive or negative appraisal by reference to emotion, and no such appraisal is enacted here. (Any enactment of a judgement by the author of the clause is a separate matter.)