There are no rules for this sort of thing. You can start your own country, if you can back it up. And if you’re just one nutty dude with a flag in a wasteland, other countries can feel free to ignore you.
You can’t buy it from Egypt or Sudan, as neither of them would claim to own it. You went to Sudan’s doorstep offering to buy it, they’d tell you to go to Egypt, as they consider them the rightful owner (so that they can have the Halai’b Triangle). Reverse the parties for the other scenario.
That’s what is creating the special situation. It’d be kind of hard to claim it anways as, while Egypt or Sudan won’t be able to give it to you, Bir Tawil is only accessible through them, and they might not want you as a neighbour.
But can’t they sell any interest in it even if they don’t claim it.
If a person came up and offered you $1000 for any rights you own to a really nice boulder in the neighbor’s yard, couldn’t you sell your rights as long as you do not sell the boulder itself and you make no fraudulent statements.