Losing power randomly

Gonna need to have it scanned for codes but the most likely cause is a fault with the 12 V battery system.
If the battery is going dead or the battery cables are loose, it can cause a whole host of strange symptoms and set random, unrelated codes.
Get the battery checked; or if it is the original OEM (5 years old) you might as well just shop for a new one.

 

You may have an inverter coolant pump problem but the code does indicate loss of 12V power.

 

Like anything else electrical, the battery can be intermittent too.
And it is hard to see brightness variations of the lights in the daytime.

Not saying that it HAS to be a 12 V battery problem but the experience of a LOT of owners suggests that it very well could be and dismissing that without getting it tested could be a big mistake.

The really unfortunate part is that the battery can test good one minute and fail a few minutes later.

 

disconnect the battery and measure it at the posts with a voltmeter after the surface charge is gone.

 

Both readings are somewhat low.
10.2 is WAY low and the charging voltage when ON should be a bit more than that too probably.
I think you are on the verge of total battery failure.

 

Replace the 12V battery now.

 

What kind of headlights does your car have?

If HID, replace the bulb now because it is getting marginal and not staying lit given the high voltage applied to it by the ballast.

A failed headlight is not going to cause your car to stall. So you need to consider that your car has multiple issues.

 

do you have any aftermarket accessories like remote start?

 

What does "eventually" mean ??
And you might have the cause and effect backwards; that is, when the car runs fine, the headlight works too.

I still think that you simply need a new, fully charged battery but when you "tap" on something and it starts working again you have to consider a loose connection somewhere.