It was only a thought, a caveat in the back of my mind. I used to have a Botswana work permit. In fact I still have the green ATPL that's probably a tad old by now. Six months was always fine for a tourist visa but somewhere in the back of the mind was the thought that, if you get there and apply for a work permit from down there, the Botswana authorities will want to see a three year validity in your passport. As I remember, but it was a while ago, the intial work permit was for a two year period of validity with an annual extension thereafter.
I cannot see that there is any good time of the year to apply for a tourist visa and I equally cannot see why you would not get one. I don't think for a second that you'd get an open work permit. You'd need a company to organise that for you I'm sure and they would have to show Home Affairs or whomever that there was no local who could do the job they had offered you.