Solved!

I'm trying to replace the light pull switch on the ceiling fan. Breaker is off, light bulbs are out.

The old switch has two black wires that run into the light socket, out of the socket comes a white and black wire. The black wire seems to be connected all the way through, the white wire obviously starts in the small socket fixture.

How do I connect these wires? Further up is a crimp connecter on the white and black wires.

I thought this was going to be easier.

Edit: pictures hopefully fixed.
I also don't have any wire nuts or similar connectors apparently so, I am running to grab that.

Edited: link to pics deleted for my sanity

I have a light/fan combo in a bathroom that are controlled with a single switch. I want to control them separately, but running a new wire would require ripping out drywall, which I don't want to do. It is in a guest room, so it can't be controlled with an app, even though I know there are ways to give guest access to certain home automation systems.

The power runs up from the floor, through the switch, and then up to the fan, so I have power at both locations. The wiring for the fan is in the attic, so putting something up there is easy.

What I imagine exists is a remote double relay that can be controlled by 2 physical switches(preferably single gang, but I am prepared to open up the wall a bit to install a double gang box). I would prefer that the relay be powered by 120v, rather than a 12v device that needs a plug somewhere, but its not a total deal breaker.

Anyone have any ideas?