1. Occupation
What I was saying is that the word "occupation" is not intended to catch both employees and independent contractors, but was used to catch both industrial or non-industrial undertakings.
As you can see, Section 68 imposes different rules on industrial and non-industrial undertakings.
What I was saying that Regulation 3, instead of saying "Subject to section 68 (2) of the Act, no child who is below the age of 13 years shall be employed in any industrial or non-industrial undertakings", the words "industrial or non-industrial undertakings" is replaced with the superset word "occupations".
2. Employed/Employ/Employment vs Employee/Employer
Whilst using the term "employ" and "employee" in the same Section, as quoted in examples raised by you, does make for bad drafting, it does not mean that there is automatically, a conclusion that "employ" has a different meaning from "employee". We can discuss the many ways drafting of a statute can be improved, but that alone is not a conclusive means of statutory interpretation.
Your case would be better, as far as statutory interpretation goes, if the Act contains a Section which has the word "employ" together with what is obviously an independent contractor, say for example: Definition of "contract for service" (as opposed to "of service") is "any agreement...whereby one agrees to employ another as an independent contractor but such that the latter is not subject to the control of the former etc etc".
However, there is no such example and I don't think you can find it anywhere.
I think you will be stretching the argument very far to say that "employ" covers both "employees and independent contractors". If so, I can easily argue, why not use the word "hire" instead? In my mind, it is simply bad drafting, rather than an intentional differentiation between "employ" and "employee".
Finally, in the Hansard for the Employment (CAYP) Regulations, the Minister makes reference to "
employers of persons" and gives examples of working in Burger King; and that "Ministry is of the view that there is no need to disallow employers from employing school children below the age of 16"- using both "employers" and "employing" in the same breath.
I also believe that the entire Employment Act was intended to cover a situation of employment (in fact only a subset of employment really), and not of independent contractors. If you can find an example of independent contractors being covered in the Employment Act, please let me know.
Of course, you are free to take a different view and we can simply just agree to disagree on the interpretation of the statute

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3. Case Law - Contract of Service vs Contract for Service
The case of a modelling agency representing a model may be less clear (although I still submit that it is not employment), but I think that you will agree that the hiring of models by photographers is very unlikely to be construed as "employment". Lets tackle this first, since what is of interest to CS here is photographers first, not modelling agencies.
I never said that the declaration of non-employee by a modelling agency is an automatic conclusion. It is however a relevant factor to be taken into account according to case law.
Whether something is construed as employment as case law has provided, follows a series of factors, such as the declaration above, whether there is control , power of selection, power to control method of work, right of suspension or dismissal, whether the man providing the services provides his own equipment, hires his own helpers, degree of financial risk taken, degree of responsibility of management, and whether he has the opportunity of profiting from sound management in the performance of his task.
If after considering the above factors, you still take the view that the hiring of models by photographers constitutes employment, do share your views on why you think this is the case, with regard to the factors above.