I really wonder how people came to the conclusion that it is a good idea to make English the lingua franca of the internet. The British alone are not sure how to pronounce things, the US citizens pronounce stuff differently in different counties, and then there are all the other places in the world, where English is a native language, too, where people pronounce stuff entirely different again.
Now, everyone should learn English, because that's a good way to communicate with everyone else in the world. However, how are we supposed to know how to pronounce things, if not even the natives actually know? Really bad. I suggest switching to an easier language... like Toki Pona.
Ee-ther? Ai-ther? ...-way, I go for /git/ and /gif/, because that's also the German pronunciation, and I know that I already talked to a ton of native speakers who pronounce it like that, so it can't be that wrong!