False negatives are much more likely than false positives. If you test positive with the rapid test and you have no symptoms, then you re-test. Or you have a PCR test. Yes, it is possible to test positive for months after you had Covid, but again, it is pretty rare. Most will test negative shortly after their symptoms cleared up.
But yes, I do get the problem of the uncertainty, especially if you are not from Cape Town and you have to lay out a sizable chunk of cash to get here.