'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.

Targeting Authority On One's Own Behalf

'Portray' As Relational Process

In Deploying Functional Grammar (Martin, Matthiessen & Painter 2010: 124), portray is interpreted as a behavioural process, despite it occurring in effective clauses, and despite its Range not being a behaviour.

'Sneak' As Happening, Doing, Behaving And Targeted Saying

The lexical choice of 'sneak' adds a Quality feature to the Process.

Behavioural Clauses With Depictive Attributes

Tagged Imperative Or Metaphorical Interrogative?

The first analysis treats this instance as a tagged imperative clause, whereas the second treats it as an interpersonal metaphor of mood: a command realised as polar interrogative clause. Cf

This raises the question as to whether the tagging of the imperative facilitated the genesis of the metaphorical variant.

Organism Competition

all organisms	compete	for resources
Behaver	Process: behavioural	Cause: purpose

This behavioural clause ascribes consciousness to all types of organisms — including bacteria, amœbæ, plants and sponges — and construes all organisms as consciously competing with each other. Moreover, it construes the result of organism behaviour — access to resources — as the conscious purpose of the behaviour of all types of organisms, without knowledge of their conscious states.

Gene Competition

genes	compete	for selection
Behaver	Process: behavioural	Cause: purpose

Such a construal ascribes both consciousness (Behaver) and intention (Purpose) to functional segments of DNA molecules.

Depictive Attribute vs Process Of Elaborating Clause

he	went	home	happy
Actor	Process: material	Location	depictive Attribute

he	went	home	smiling
Actor	Process: material	Location	depictive Attribute

he	went	home	smiling	all the way
α			= β
Actor	Process: material	Location	Process: behavioural	Extent

Emotion-Imbued Cognitive Projection

I am unable to look at my customer in the dock	without feeling	there but for the Grace of God goes Horace Rumpole
α	+ β
	1	' 2

I	am unable to look	at my customer in the dock
Behaver	Process: behavioural	Location: orientation

without	feeling
	Process: mental: cognition

there	but for the Grace of God	goes		Horace Rumpole
Theme: marked	Rheme
Location	Contingency: default	Process: material		Actor
Attribute: circumstantial		Process: relational		Carrier
Adjunct	Adjunct	Predicator	Finite	Subject
Residue			Mood

The above analysis assumes the Mood Tag would be doesn't he (rather than doesn't there).
This analysis is supported by the phonological salience of there.