Didn’t Nicola Tesla had papers and work of his made classified?
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Yep:
You know, if the US government had a working Death Ray, wouldn’t we have used it against the Russkis?
I think you mean the Fourth Amendment. The Fourth is unreasonable search and seizure. The Fifth is due process and self-incrimination.
I do not.
I’m not sure if this falls under taking private property, but researchers in encryption techniques at one point had to have papers vetted, even if not funded by the government. So that’s another category they find of interest.
The important distinction in terms of national security is exactly what the OP says: “A Guidance System.” Not a weapon system, or a previously unheard of technology. Nothing potentially classified about that at all. They’re everywhere, in all types of vehicles, land, sea and air, to include missiles. Even your cell phone (GPS). Just because you attach it to a missile with a nuclear warhead doesn’t necessarily make the guidance part classified, in and of itself. It may also be used to guide a toy rocket.
Many classified government systems are comprised of multitudes of bits and bobs that by themselves are not classified. Only when the Defense Department gets a bunch of this stuff together in a weapon system or some newfangled technology breakthrough does it sometimes become classified.
To answer more specifically, however: YES - if you are already working in a classified government program.
Me personally? Yes. But it’s part of the job 
Not if analysis of the “ray” itself or its effects would have made it too easy to duplicate. Better to keep it off the table and unknown until it comes down to backs against the wall.
Well, that is outside the OP. You are being paid by the Government (I am/was in the same situation) and whatever discoveries you make, the Government gave themselves first dibs when your company signed the contract.
As for the OP, I have a slight hi-jack. What if any laws would one be breaking if one published/demonstrated a new technology that the Government would like to be classified? Assume no Government funding, no patents, no Government support at all. I just take my shiny new anti-gravity vehicle and do a few fly-bys in front of some news cameras. The Government won’t like it, but did I break any laws?
The FAA might have something to say about it…
Timely. The FBI has just released their Tesla files.
One thing to note about the Invention Secrecy Act, is that it actually doesn’t prevent the information from getting out. If you aren’t interested in patenting something, you can just release it without any apparent problem.
If such information was truly deemed to be kept a secret no matter what, then the law would have to comprehensively prevent all such disclosures. And good luck with that.
I will keep the fly-bys under 1000 feet. 
It’s often said that three people can keep a secret, assuming that two of them are dead. In other words, it’s all down to information control.
If someone were to invent a new, potentially disruptive technology - a new way perform decryption, for example, well, that would be of great interest to the government. But, filing a patent necessarily makes that discovery public. So, the patent would need to be classified straight away, before it’s approved. All research (and any scholarly articles) leading up to the discovery would also need to be reviewed & possibly classified. The owner of the technology would have to be kept silent.
If the researcher(s) were to publish their findings before filing for the patent, I can’t imagine the utility of seizing or classifying it. In fact, if memory serves, there was a Keanu Reeves film about this exact scenario. (Chain Reaction)
The practical application of technology in terms of new devices, machines, processes and practices, including the design details and related information is typically what gets classified - not the technology itself. Everyone knew we had stealth in the late 80’s, just not exactly how it worked, materials and specifications, etc. Even now, the Chinese and Russians struggle to catch up because they know the technology and how it works, just not how to make good, working jets with it.
If it’s that easy to duplicate, then it’s an obvious development that will be discovered independently soon. And then you’re going to be the one scrambling to keep up as the Reds are blasting everything that moves as they roll through the Fulda Gap.
When you look at the history of technological development, there are no deep dark secrets. When the North Koreans have trouble making nuclear weapons it’s because the processes are extremely complex and have to be done precisely, not because the technology is secret.
All the stuff that Tesla supposedly invented but kept secret was just bullshit. Invention doesn’t work that way. Yes, there are unknowns in past engineering. For instance, we don’t know how Greek Fire worked, exactly. But that’s not because Greek Fire is based on super-science that we can’t duplicate, we could duplicate Greek Fire in dozens of ways, we just don’t know the particular method the Byzantines used.
Tesla invented some stuff, and he also made up a bunch of bullshit to impress the rubes. If he had invented a Death Ray in the 1920s, his work would have been duplicated by others, because the laws of physics work the same for everyone.
Phil Zimmerman was almost charged with munitions trafficking for releasing source code for PGP encryption/decryption.
(IIRC, some other mathematics graduate student was so charged for a paper on cryptology — am I misremembering?).