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So far I have not seen a factory turn signal switch without the "Auto" setting on the turn signal arm. If I swap one of these into my LX, what happens when I turn it to "Auto"? Currently, I don't have that.
The Honda accessory fog light kit was only for 4 cylinder EX and EX-L trims. Your LX is not pre-wired with part the harness and connectors to connect to the fog light accessory kit. Also, adding a switch that has a setting for auto headlight won't make a car that is not equipped with it change into auto.
For example, the following are what an EX and EX-L has pre-wired: