Hey Scotty, I bought an aftermarket fog light kit for my ‘19 Ram 2500. The wiring harness came attached with a switch to toggle the lights on/off. I instead want to wire the lights to my factory Auxillary switch. So I have a Red for the power, Black as ground, and a White that comes off the relay to the aftermarket switch. I’m thinking I’ll cut off the white wire at the aftermarket switch (agin since I’m using the factory auxillary switch to toggle on/off) and tie that into the red/power wire.
Does this sound correct? In doing so, this won’t cause a draw or drain on the battery work it?
You want to use one of your Aux switches and built in Aux relay instead of using the switch and relay that came with the fog light kit. Great idea. It'll make for a nice clean installation.
Here's a generic diagram for an aftermarket fog light kit.
The only part of the kit you'll be using is the part I have inside the purple dotted line.
The lights, the ground wire and the power wire.

Let's say you want to use the Aux1 switch for your fog lights.
That load side of that circuit is protected by a 40 amp fuse and has a relay which is energized when you press the Aux1 switch.

To compare what you'll be doing look at that generic wiring diagram I posted.
The Red wire from that aftermarket relay pin 87 that powers the fog lights will now be connected to pin 87 of the Aux1 relay.
You access the wire that connects to Aux1 relay pin 87 at the upper Aux wiring connector. It's the connector terminal on the upper left.

Ideally you'll use the wire that came in the bag with those Rams that have Aux switches.
If you can't find it you should buy it because those wires are made to lock into the connector and have a weathertight seal so no corrosion forms inside the connector.

So just disconnect the connector, pull out the rubber plug, click in the wire (you have to lift the lock bar inside the connector and then push it back down when the wire is in), reattach the connector, and splice the Power wire (that originally went to pin 87 of the fog lights aftermarket relay) to this wire.
Then select a good Ground point for the fog lights Ground wire and you're done
Thank you!