I'm not sure I understand. Action is shown, but I don't see how it can be called a clause. A clause has a verb. The phrase "after eating dinner" has a "verbal", which is not exactly the same as an "action verb".
In the example,
after eating dinner,
eating is most definitely a verb. Moreover it is not part of a postmodifying structure (see below).
Every VG that is not part of a postmodifying struture is known as a Process. Every clause has one and only one Process, and every Process is part of one and ony one clause. Postmodifying structures (see below) are referred to as embedded clauses, but they are not "true" clauses, because they are only part of a nominal group (eg see below -
beer that's cold etc ) and the VGs they contain do not refer to the actions or relationships that the text is immediately concerned with.
Verb Groups (eg: go, went, had gone, was to have been going, eating, had eaten, ate, will be eating, would have been going to be eating, say, would say, had thought, is, was, would be, has, had been, had had, had been having, there is, there will be...etc etc etc etc etc etc) are used in English in one of two ways.
1. As Processes
2. As part of modifying structures (embedded clauses)
Examples of clauses containing VGs as Processes:
(the following examples include Dependent, Independent and Nonfinite Clauses)
after eating dinner/when i go to town/ I am here/ we would have to go there/sit down here/ because there are two of them/there is never enough time/ having realised the implications of this/
these are the chairs/ i don't drink beer
Processes are VGs that are of immediate relevance to the action, the events, the relationships or the situation the text is concerned with.
Examples of VGs as part of modifying structures
the chairs that they sat on/the one you like most/beer that's not cold
Examples of Clauses with VG in the post modifier
These are the chairs that they sat on.
Choose the one you like most.
I don't drink beer that's not cold.
It is of great help to students to be shown how to distinguish between VGs that act as Processes and those that act merely as part of a postmodifying structures. This can be acheived by firstly asking them to identify all VGs in text, then to identify which are Process and which are not (ie which are merely part of Nominal Groups. They can then proceed by identifying clause boundaries, and then further to discriminate between Independent and Dependent Clauses, and to recognise and understand how they are connected.
A typical analysis would go like this:
Example:This is the table that we had been going to buy on that trip to China when John was writing that new book of his that sold so well.
1.
Identify Verb Groups:
This
is the table we
had been going to buy on that trip to China when John
was writing that new book of his that
sold so well.
2.
Identify which are Processes and which (merely) modify.
.........Proc..............................Modifying
This
is the table we
had been going to buy on that trip
..................................Process................................................Mod.
to China when John
was writing that new book of his that
sold so well.
3. Identify Clause Boundaries and clause types.
INDEPENDENT CLAUSE ( includes <<Postmodification>> of table)
|||This
is the table <<we
had been going to buy on that trip
to China>> ||
DEPENDENT CLAUSE (includes postmod of "book of his")
|| when John
was writing <<that new book of his that
sold so well>>.|||
Systematic analysis of text in this way (these are just the first few steps) gives students of all levels the tools to analyse and come to understand the fundamental structure of English. I know because this is what I do.
There is nothing fundamentally "wrong" with traditional grammatical approaches. It's just that they are really quite meaningless where English teaching is concerned. English , indeed any language is not the sum total of millions of individual fragments as traditional grammatical approaches so wrongly imply. Rather languages are comprised of discrete functional units of meaning, and it is these for which students are searching in their endeavours.