I cannot answer you on your question, but knows it is even more of a problem when you are on Botswana side.
End of September this year a couple (~ 60 years old) was stranded near Swartpan due to their car battery running flat and they had no means of starting the vehicle. Luckily some-one passed them, but were reluctant to help them to jump start their car incase of a short and both cars will be stranded. They had no Satelite phones and the only way out was to get help from the nearest camp.
I am not sure if they tried to get help from Kaa gate, but help was request from Nossob camp and Botswana parks. At first the person could not get any one to come out with a tow truck or mechanic to help and in the end called it a medical emergency. Finally the couple was helped by a team from Botswana defence force at a great cost.
I think in case of a life-threatening situation you will get help, but if you want to make the call it will be best to hire a satellite phone when you further north than Twee Rivieren.
Quote form 4x4 Community Forum:
What happened was that, at Swart Pan, (booked for 6 days) we ended up with two flat batteries, two slow punctures and one other flat tyre ""repaired" in Vic Falls. (Slow punctures as a result of reversing full speed for 130mtrs from charging elephant at Bumbusi Waterhole - with armed ranger in our vehicle.) Hand pump was difficult to use in soft sand so also used cigarette lighter pump. I put in one plug which worked. Also had to drive to keep Engel battery charged, but obviously- not enough revs. (battery!) Maybe need a solar panel.....
A person at camp 2 used our jumper leads, but he was afraid of damaging his sophisticated Discovery engine. (he had prev been flat-bedded out of Kaokoland....) He left and I req him to contact Nossob. He tried 9 diff numbers supplied by phone Co and passed on from pillar to post by previous number - Nossob Camp, SAPS in SA, Bots Police in Tshabong, DNPW Gabs, Dnpw Kaa, (no vehicle) and the they contacted BDF) for 45 min and eventually in desperation, he declared it a "med Emergency" - he was being shunted from pillar to post and needed someone to react. Three days later BDF came to help us start. Had food for 10 more days, 35ltrs of own water, and a sweet-water tap at Swart Pan. PS., We checked beforehand on other bookings for S.P. - there were, but they did not arrive. Satfone? Don't think so - lots of Hyltons around to help sometime whenever wherever... Barry 63 and Dorothy 65.... "old" . Thanks and happy driving.