Monocular

I like that flaw, and I've played a version of that before, but there is something that goes against common sense: shooting with a range weapon usually requires someone to close or use only one eye to aim accurately, whereas melee combat requires good depth perception to be effective (i.e. two functioning eyes). Based on that, I would give disadvantage on melee combat, and no disadvantage on ranged combat. What do you think?

That's true! It could potentially be disadvantage on _all_ attacks. Though that is a really, really strong penalty to apply for a feat.
Part of me feels like the depth perception shouldn't be too much of an issue within 5ft though, unless you're fighting purely with the tip of your weapon.
Maybe it could instead be something like disadvantage on attacks with piercing weapons?

In today's world of high-powered guns and rifles, being monocular wouldn't hurt too much.
However in medieval times when archers had less powerful bows/crossbows that required you to account for gravity and wind, having poor depth perception would have severely harmed your ability to aim.

Having trained as a fencer for over 15 years, and practiced archery as well, and having lost the use of one eye for over a month due to illness, I can tell you from personal experience that losing eyesight from one eye definitively trashed my fencing ability, but didn't affect shooting with the bow at all – with a very standard shortbow. Granted, the affected eye was not my dominant eye, so aiming was not more difficult than closing my weaker eye. On the other hand, something as simple as going down the stairs felt tricky and almost dangerous. After a couple weeks, I had partially adapted, but I was still feeling uncomfortable due to losing 50% of my field of vision (and perception). Gaining back the ability to see with both eyes felt amazing.

Another side effect of the eye patch was how it affected people who met me for the first time during that month: definitively improved my Charisma ;)

To get back to the flaw: instead of the penalty to attacks (ranged or not), another path to explore with this flaw (on top of the penalty to perception checks and passive perception) is a penalty to Acrobatics checks: trying to be accurate with your body movements can be difficult with only one eye. So a -1 to Perception and Acrobatics would make sense. I think removing the malus to combat would make it easier to choose this flaw, since it can be so crippling so often.