How can I add a tilt button to a Brook Fighter's plus audio for a hitbox?

I want to use 8 buttons for the two analog sticks.

They use 10k ohm to 0 ohm. So I’m assuming I need to a 5k ohm resistor in series, and then halve the value by the button.
What I don’t is how to do that when the button is a pot.
If you connect a resistor of the same value in parallel, the resistance is halved. But how do you give that value when it can constantly change?