Section 33 of the Basic Conditions of Employment Act requires your employer to give you written particulars of your pay at the workplace, during working hours, on or near the day you are paid. It is not optional and there is no size threshold below which it stops applying. A household employing one domestic worker is covered by the same section as a company employing four hundred people.
Being paid in cash makes no difference either. The obligation attaches to the payment, not to the method, so an employer who hands over an envelope still owes you the written breakdown that goes with it.
If yours will not provide one, the route is the Department of Employment and Labour rather than SARS. You can lodge a complaint at any labour centre, and an inspector can issue a compliance order. In practice, asking in writing and keeping the reply resolves most cases, because the employer is usually not refusing so much as not doing it.
One thing worth knowing if you need the payslip for a loan or a lease: most South African lenders and letting agents will accept three months of bank statements instead. It is worth asking rather than delaying the application while you argue with a payroll department.