Which photo has the more correct White Balance? For me the second is much better than the first. My understanding is that the R+G+B histogram needs to be as balanced as possible. Is this true, or does it depend?
Like with photograhps in general, it's down to opinion and there is no real "correct".
Here's is a table of typical light source scenarios:
In processing the image, whether in camera or PP on a computer, it adjusts the overall colours of the image to look more redish or blueish.
In your particular image:
The original image shows no clear overall redish or blueish, so it's hard to tell. It may not even have needed WB adjustments but the first one has a slight red tinge to it in the "silver" areas. In my opinion, the first one is better and didn't need adjusting however, the second is more "silvery" because of the more blueish tinge. It neutralised the grey areas more.
Without referencing a white object in your photo, we cannot decide which one has a better white balance. In short, white balance is process of removing unrealistic color cast on your image, i.e., correct the white area in your image that captured as gray. So it cannot be judged by histogram. If you know what part of your image should be white and the image is not affect by other light source, you can adjust the rgb balance in your image until the white part has a balanced rgb value.
The technically correct white balance setting is the setting that "cancels out" the color of the lights lighting your scene so that the color of items in your image is the same as the color in real life.
You can't judge white balance from the histogram or anything in the photo without some reference to that item real color (that's how the white balance "eye dropper" works - you tell him that the specific color in the image is actually white or neutral gray and it re-calibrates the entire image around it).
And finally, unless you are shooting products or photojournalism you don't have to limit yourself to the "technically correct" white balance, playing with white balance can create very nice effects (especially if you have multiple lights with different WB and you set them up intentionally)