Inside your mouth is not a legal target

Only points in space or objects are legal targets for darkness — since the inside of your mouth is part of you (a creature), you can’t cast it there.

Your PC’s mouth is also likely not opaque

You could fix the targeting by casting it on a marble or similar that you could place in your mouth after the casting, but then you have the problem that your mouth is unlikely to count as “opaque” by any of its senses (except the irrelevant one that describes an object’s shininess):

opaque, adjective

1. not transparent or translucent; impenetrable to light; not allowing light to pass through.


2. not transmitting radiation, sound, heat, etc.


3. not shining or bright; dark; dull.

The combined skin and lining of the human mouth is translucent, in that it permits light (but not distinct images) to pass through. Elven, gnomish, and etc. mouths are not known to be different from human mouths in this regard either.

As a way to get a “free” (and therefore infinitely-usable per turn) toggle control on darkness, it’s highly questionable.

A dragonborn's scales might make their mouth opaque — check with your DM about this, but mind that contrary to appearances, scales are often translucent like skin, too. Even then, also mind that you'll likely still have to use the action economy as below, anyway.

How to toggle darkness for cheap, but not free

You have one item interaction per turn that won’t cost an action. Any scheme for toggling darkness will use that, even if it's in a somehow-opaque mouth, because of the aforementioned game-breakage.

So, to toggle darkness in a way that any PC race can use and keeps the game intact, just secure your marble to the inside of a small light-tight box tied to your belt; use your free item interaction to flip it open or closed.

That’s as big as this exploit really gets, and it’s not that powerful.

This would violate the Object Interaction Rules

In 5th Edition D&D, you're granted 1 free object interaction per turn, limited to only simple interactions. Opening your mouth probably counts (to make the object visible) and closing it probably also counts (to make it obscured) but doing both in the same turn would require you to use the Use an Object Action.

It might seem strange, but mechanically, it's not requiring (substantially) more effort than lifting said rock out of your pocket + putting it back.

A Thief archetype Rogue might have an easier time of it

Thief Archetype Rogues gain the Fast Hands feature at level 3, permitting them to perform the Use an Object Action as a Bonus Action instead. So theoretically, as a Thief Rogue (multiclassed with whatever class gives you Spellcasting abilities), you could

• Close your mouth (Free Object Interaction)


• Cast a Spell or make an Attack (Action)


• Open your mouth (Bonus Action)

You could also do something less disgusting, like putting the rock inside a latched box that you then open + close using this sequence.

Some DMs are particular about the Simultaneity of Combat

Because the separation of combat into distinct "turns" is meant to be an abstraction of real-time combat, some DMs interpret this as meaning that it's not possible to meaningfully "strobe" an effect like this without some delayed interaction (i.e. a Reaction used on someone else's turn). The degree to which this is RAW is hotly contested, but this is a common interpretation of the rules.

So as a result, some DMs may rule that this is what actually happens:

• You close your mouth (Free Object Interaction)
  
  
  
  
  • The Darkness effect may or may not vanish, depending on what happens before your turn ends
  
  
  
  


• You make an attack or cast a spell. If you open your mouth later in this turn, the attack is made with Disadvantage, or the spell must not require visibility of the target


• 
  If you open your mouth the Darkness effect doesn't vanish.


• 
  If you instead choose not to open your mouth, the Darkness effect does vanish (becomes obscured by your mouth) at the time you close your mouth (???)

Again: I am not certain that is a RAW ruling. I'm just informing you that that is a ruling many DMs make.

Human[oid] biology is disgusting

Strictly RAW, the Darkness effect spreads around corners, and so long as there is an unbroken path to all points within its radius, the Darkness spreads to that point. So some DMs may rule that the inside of your mouth (which is connected to your nostrils, even your ears to a degree, through your windpipe...) does not adequately obscure the Darkness effect. This may vary depending on the creature's race, but 5e doesn't describe in precise detail how the anatomy of other Humanoid races vary from the anatomy of humans.

While opening and closing your mouth might be free, timing it such that you don't hinder your allies and blind your enemies in the exact moment they take aim looks complicated enough that you should not be able to do it freely. Also, this may not prevent the enemies from delaying the attack until you close the mouth again, effectively having them attack first as soon as vision is restored (thus not having any practical effect in the attack sequence)

I don't think it would work, at least for most races. Per the Darkness spell:

Completely covering the source of the darkness with an opaque object, such as a bowl or a helm, blocks the darkness.

Oral cavities are not opaque (try putting a flashlight in your mouth), and I'd extend that to all normal player races. I could see this working with, say, a stone golem.

If your mouth is "opaque" to the effect, then you can use this as you see fit, but prepared for weirdness if you try to talk with it in your mouth.

That said, and especially given that I suspect you are the player cited in the question How do I deal with players persistently arguing for rules loopholes, even after I've tried to finalise my rulings?, you must always be prepared to abide by the top rule in D&D, that the word of the DM is law.

So, regardless of what the rules may or may not say, if your DM says different, what he says goes period. This how to play:

1. The DM describes the environment.


2. The players describe what they want to do.


3. The DM narrates the results of the adventurers’ actions. (Basic Rules, page 3)

So it partly depends on how tolerant your DM is of players thinking outside the box.

If your DM overrules you, then, regardless of what the books say, show them the respect they are due as DM and comply with their rulings.

TL;DR: This would work, but I think you're overestimating how powerful it is.

This sounds like it would work, in the basic sense. The description of the Darkness spell clearly indicates that the darkness can be blocked and unblocked at will. Another answer objected to hiding it in your (natural) mouth specifically, but that seems like a trivial distinction to me (you could easily work around it by rigging up a contraption of some sort, for example a bag in your mouth attached to your teeth).

Flavor-wise, the image of darkness spilling out of your mouth to fill the area around you is awesome for an Evil character. It also implies a certain delay as the darkness spreads like a mist. This would give the DM a good excuse to nerf it, but such a nerf wouldn't be RAW.

Either way, the unreliable light from the Darkness spell being off some of the time will clearly be enough for every creature to know where every other creature is located, so the darkness will serve only to give a penalty to attack rolls. However... the fact that you also can't see the person attacking you gives you a penalty to defense... so the darkness might not have any effect on the combat at all.

• At the start of your turn, you close your mouth.


• Everyone (including you) can now see clearly. Combat proceeds as normal.


• At the end of your turn, you open your mouth.


• Everyone still remembers where everyone else was standing, so they have no problem attacking the correct locations.


• Any attacks made in magical darkness have both advantage and disadvantage, so they're made at normal success rates.

If you're clever about opening your mouth before an ally moves so the enemies have a chance to target the wrong location, this might be helpful. If you strictly open your mouth at the start of your turn, it seems rather useless. Overall, this doesn't seem OP to me.