Namibia: Traveling visa free to collect ill relative?

I would normally call the embassy in question to ask this, but they are closed for the weekend and I am in a slight hurry, so I am hoping someone here might be able to shed some light.

My father has just had a heart attack in Namibia, and as I live in the United States I am the closest person in the world to Africa in my family. I would like to go to the hospital he is in to collect him and take him back to Australia.

Although this is not a vacation, would this fall under the "holiday" exemption for having a visa? I will not be working when I am there.

I will likely not have a return ticket booked on arrival, because I do not know how or when I would be leaving. I also do not know how long he will need to be in the hospital before he can leave, and I do not know which airline he would be flying to leave (He will already have onward travel plans on a flexible ticket, so I assume when he is healthy he will be able to use that ticket). I suspect this would be on the order of days or weeks, not the three month limit on visaless entry.