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Ok, so let me see if I've understood this.
The Sun is basically a spotlight that shines 'down' on the face of the earth, and it doesn't 'set' it just gets further away, right up until the point where it no longer shines down on my bit of the earth, and it gets dark. Is that right?
So, things that get farther away tend to look smaller as they do so, but because of 'atmospheric lensing' the sun actually looks bigger as it gets further away, right up until it can be seen anymore and it becomes dark?
In your setting sun example, the sun is about to drop out of your visual reference field, as it gets closer and closer to appearing at the same level as the ground. It is this lower level where the atmosphere is the most dense, heaviest, thickest as well as different temperatures which gives the impression of the sun "getting bigger". The sun didn't get any "lower", it's just moving beyond your visual field. It remains at the same height. That it looks bigger to you is essentially the atmospheric lensing effect. There are other explanations for seeing the "Big Sun" in Africa out on the Serengeti, for example. Those have more to do with the time of year and the transiting of the sun between the Tropics.
Now compare and contrast this to standing on a 1000 MPH spinning ball rotating around a stationary ball of hydrogen gas at 66,000 MPH. Why would the sun appear bigger at any stage in this globe model? Nothing is "changing size", right? So why the "appearance" of a change in size then?
So, how does the setting sun often highlight the underside of clouds during a sunset then, if everything I'm seeing is just a trick of perspective?
That's called the "cloud deck". Again, it's a function of perspective.
How would you explain it differently regardless of whether ball or flat earth? Same difference, no?
"Cloud Deck" isn't an explanation, and I have no idea what it has to do with perspective.
Either the light from the sun is lighting up the underside of the clouds or it isn't. I don't see how my perspective would change that.