I haven't looked at the Eaton wiring schematic but a simple SPST on-off switch should work well and from your photo it appears that is all the Eaton switch is. At least I only see two wires going into it.The auto locker will work fine most of the time. But that one time when you really wish you were in control, you won't be. I would (and did) go with the E-Locker for Colorado driving.
The switch which comes with the E-Locker is enormous. Instead of trying to mount that monster, I used a GCD switch which snaps into the switch bank on the dash:
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https://www.amazon.com/dp/B08HM97SW9/?tag=wranglerorg-20