The spin-a-split feature isn't controlled by a switch, it's controlled by a pot.
Here is an example diagram of the concept, just a basic barebone setup w only one pickup so you can get an idea of how a spin-a-split works.
For your HSS setup specifically, you're going to need to either install an additional pot, or convert one of the two tone pots to a Master Tone pot for the guitar so you can use the freed up pot for the spin-a-split, or replace one of the three pots with a dual concentric pot (which is two pots in one), and wire 1 of its 2 pots to function like the Tone or Volume pot you removed, and the other to control the spin-a-split. For that last option that uses a dual concentric pot, maybe a more elegant arrangement is setting up the two pots of the dual concentric as Neck Tone and Middle Tone, and then the one original tone pot that remains installed, gets rewired to control the spin-a-split.
Forum member Clint55 who is a big fan of the spin-a-split feature advocates using a pot whose value is 50k or 100k, can't remember which. But the point being definitely far less than the typical 250K and 500K pot values. The reason being that at the bigger values, the size of the range on the pot's sweep that changes from both coils active to one coil fully cut is too small to dial in a good spot. Oh, and he advocates for using a No Load pot as well. Maybe he'll chime in here.