No, you can't prove a negative and no, you can't know with 100% certainty. The latter claim is easily shown by the possibility that everything might be an illusion, a matrix scenario, brain-in-a vat etc. You can't even know 100% that the draw exists, so how could you say that it is scissor-less. There is always a tiny possibility that something might be wrong.
Now the former claim. In your example with the draw you don't prove a negative when showing it to be empty. You make a positive claim about the inside of the draw. If we could observe the whole universe at once somehow we could prove that something doesn't exist but only observable things that are inside of the universe and prove only in relation to the observation that could be faulty.
The difference between agnostic and atheist is most often only a definitional difference. Agnostics don't hold the believe that a god exists, which in my book is an atheist. 'Agnostic' only means that you can't know it. But some people for whatever reason don't want to call themselves atheist.

"Why else would you give it any thought at all?"..... My only observation is that it seems to me that you just did that.

I am perfectly happy to be a staunch atheist who knows that there is no divine authority as alluded to by all sorts of religions.
Religious people are true agnostics because they just believe rather than know.

Define a god and its conditions of existence/non-existence and we'll go from there. Most claims of gods or godly beings are so objectively and patently ridiculous that they can be dismissed outright, as they are presented not only without evidence but without substance, i.e. entirely untestable/undectectable.

The idea of a g-d is just ridiculous.

How could he/she not threatened to pull the car off the road if we kids didn't shut the fu-k up and get along?

"I will SHUT this ENTIRE water park day DOWN!"

"Do NOT TRY ME!"

"Give your brother a juice box, Jimmie. He's looking gray around the eyes."

Jay and Bethany

I'm an atheist. It means without a god. I don't call myself an agnostic because it often implies uncertainty. Could the Universe be part of a super particle? Sure. But it's not worthy of considering given that the reason to think that there is comes from anything worthy to pursue it.

I don't have a worthy reason to believe that God exists anymore than the super particle. Agnosticism would mean there is a super particle.

Agnosticism is a lack of knowledge that a god exist. Not all agnostic believe there is an afterlife. I'm an agnostic atheist.

With regard to the scissors if it was a ‘boy’ look they probably are in the drawer!

Possibilianism is something I subscribe to overall. Possibilianism is a philosophy which rejects both the diverse claims of traditional theism and the positions of certainty in strong atheism in favor of a middle, exploratory ground.
To quote who came up with the term "Our ignorance of the cosmos is too vast to commit to atheism, and yet we know too much to commit to a particular religion. A third position, agnosticism, is often an uninteresting stance in which a person simply questions whether his traditional religious story (say, a man with a beard on a cloud) is true or not true. But with Possibilianism I'm hoping to define a new position — one that emphasizes the exploration of new, unconsidered possibilities. Possibilianism is comfortable holding multiple ideas in mind; it is not interested in committing to any particular story."
I apply this not only to religion but everything. Evidence for/against, hell we think we have little left to prove and discover but a picture of a black hole and scientists making vaccines much more expensive, scientists who got past our fear of resistant bacteria by creating, from horoscopes to stardust theory, this disproves things like healing crystals but explores as a species are learning how to use placebo and better understand the effect. Dieties are extremely improbable and forms of atheism have been around as long as religion. Evolution is prov
I think a lot of agnostic people aren't comfortable with either idea. The more I learn the more 'atheist' I become but also the more full of wonder I become. An issue I have is people stay surface level and stops at the first step of no god.

The only thing up for debate is what started the universe. But it seems very likely to me one day or species will figure that out too. Thus, I'm atheist.

The text that claim a deity can defy the laws of nature and physics should be enough to end the debate if such absurdity existed. Sex is a glandular thing and physical concepts, thought and contemplation of such things could never be compared.