Yo, interesting question I'd claim: What do you think it means visually when written "His smile didn't reach his eyes." I've been reading some popular phrases and trying to imagine what they'd look/sound like in real life, and this is definitely one of them.
Oh, that's actually a really good question and I can answer it on two fronts: one from using the phrase fairly often in my own writing and one from actual remarks I've gotten from my time working in customer service/retail!
On the first front: typically when someone writes the phrase 'their smile didn't reach their eyes' they're referring to a smile that is fake in the malicious sense. I.e.: someone putting up a warm or happy smile but you can see in their eyes that they're up to something or that the gesture in their mouth has been well-practiced while their eyes are showing the truth.
However, there are the times when the smile is false but the eyes are genuine in cases of sad or solemn characters trying their best to not drag everyone around them down. These would include: a leader who has just lost a beloved teammate but they're desperately trying to keep up a strong front for the rest of the team, even though the tears in their eyes are washing out their attempted smile
Or a character who is suffering from depression but doesn't want anyone to ask about it so they're keeping up a practiced smile though you can look at their eyes and see it's a mask.
On the second front, though: I actually had my own encounter with this. It was back when I worked in the 'healthy living industry': it had been a long day and I had kind of exhausted all of my cheer and 'kiss-ass-ness' for the day. This group of gym-bros came in and carried on whooping and hollering and asking stupid questions (because, obviously, since I was a thick girl I know nothing about workout regiments and supplementing).
They finally came to pay and I was smiling, doing all the pleasantries, etc. But then the dude who was in charge of paying looked at my face and said 'Wow, you are completely dead inside, huh?'
To which I promptly replied, 'Yep! Your total is $298.38!'