Important:
This answer is based on tax law for the tax year ending 28 February 2020.
Answer:
As the taxpayer concerned is a sole trader the individual must base the deduction on actual costs (section 11(a), (d), (e) and 24J) actually incurred and make an adjustment in terms of section 23(g) for the private use element. It is NOT possible to use the costs published by the Minister in the (annual) Regulation. These are not available to a sole trader. This applies to the simplified method as well (the 8 000 kilometres that you refer to).
You are correct that the adjustment, under section 23(a) or 23(g), in respect of non-trade related travel must be based on a log book.