IMO driving with fog lights ONLY is not enough in fog as you are not visible enough.

Slowing down and being careful is what you need to do.

That has worked for us throughout 59 years of accident free driving
adjust speed related to road conditions is where it's at

have a nice day cheers

poor man's DRL
 

A plastic bottle cap placed over the daylight sensor will turn the headlights on during the day as long as the light switch is in auto mode.
Is this not the same as DRL only brighter?

Using your bottle cap idea it not the same. You will also have the running lights tail front and side marker lights on, and also if in the automatic setting; the fog lights on too, the head lights off delay will be enabled, and if your dimmer switch for your dash lights is set to a lower night time setting; you will not be able to see the radio, temperature and other dash controls, as they will dim for night time driving. Because turning on the wipers does the same thing as your bottle cap idea, I have the same issue with seeing the controls on the dash if I turn on the wipers during day light hours.

And if any type of inspection was needed to make sure they work, it would not pass.

update
 

I took my 2014 Navigator in for service and had them activate the DRLs.
They charged me $129.

So what exactly are the special words? It would be helpful to know.

Ask to have the day time running lights (DRL) enabled in the Smart Junction Box. (SBJ)

Many of the electrical functions are triggered by other actions, for instance when you hit the key fob to open the door not only does the driver door unlock the interior lights come on. The SBJ handles this.