You didn't say what you want the other positions to indicate. I assume it's something? Otherwise, one position is a dummy position...
The generic way to interface this and read all 3 positions in software, is to ground the middle contact, each outer contact goes to an input configured with a pullup resistor.
Then, in the "upper" position, the "upper" input is low, the other high. In the "lower" position, the "lower" input is low, the other is high. In the middle position, neither input is low.
0b01 = lower
0b10 = upper
0b11 = middle
In fact, judging from your diagram, this wiring already exists and you only need to interpret "LSP SD" and "Backlight" inputs in that way. Probably, but you should check, those inputs are already pulled high by a resistor.
So the input condition for the middle position is:
(backlight == HIGH and LSP_SD == HIGH)