Would they just appear or would there be say a streak of light?
The first thing to realize is that gravitational field propulsion is a principle and not a specific type of technology like a jet. So just as the principle of reaction propulsion gives us a wide variety of flying devices ranging from helicopters to jets to rockets to parasails, gravitational field propulsion covers a wide variety of possible applications. We've only discovered two theoretically possible forms of it so far, and it's reasonable to expect many more to be discovered over the centuries ahead.
So not only are the observational signatures going to vary depending on the application, but the rate of motion will also modulate the observable characteristics. That's why there's no single answer to your question.
But given what we've seen with thousands of AAV/UFO sighting reports, it appears that lots of UFOs perform like the Tic-Tac in the USS Nimitz CSG incidents: they don't appear to generate any significant propulsion signature. Others appear to glow brightly in the atmosphere, but that appears to be an atmospheric ionization effect - in space there would be no radiant signature because there's no significant gas to ionize. UFOs would therefore be about as difficult to observe as a small dark rock - in other words, they'd be virtually impossible to detect with any modern astronomical technology.
They probably are detected with some regularity via the global military space radar surveillance networks, but the military has been FOIA'd for these "uncorrelated target" records and they've always refused to release any data about them.
I am puzzled why, if we are visited, we have not seen ships in the solar system. Do they transition behind a planet or moon then cloak?
We don't have the tech to observe small objects navigating the solar system unless they leave a long glowing trail of reflective gases and debris like a comet. Remember
that 66ft meteor that exploded just above ground in Russia back in 2013? Nobody saw that coming until it was burning across the sky.
Which begs the question of why would they hide? At that distance we are no threat.
They don't seem to be hiding - people see them all the time. They simply just don't seem to like us enough to drop by for a spot of tea.
Do they think we would be able to work out the physics of their propulsion? or that it would be destabilizing for us?
Or is it nothing to do with us and being uncloaked is intrinsically dangerous?
Nobody knows what aliens think, but if we survive as a technological civilization I think it's inevitable that we'll replicate their propulsion technology. That probably will be destabilizing, because we humans use all technological advancements to perpetrate mass murder upon each other.
There are a lot of reports of cloaking and decloaking UFOs, so they seem to have that capability when they want to use it. That's pretty troubling, because we know that their propulsion systems are typically totally silent, and the craft themselves seem to elude most radar systems when they choose to - so they could be hovering right over your house right now and you'd never know it. I take comfort in the fact that I'm not interesting enough for an advanced alien being to spy on, but it's disquieting to realize that they could be all over the place and we'd never know it.
I've come to believe that there is no technology capable of propelling a ship across the vast distances in space in a conventional manner.
It depends on what you mean by "conventional." Gravitational field propulsion isn't "conventional"
to us, but apparently it's commonplace among more advanced civilizations. And it violates no laws of physics. So apparently that's what they're using: not primitive rockets, but rather spacetime distortion technology which is indeed permitted by Einstein's general theory of relativity. Someday we'll use that kind of technology ourselves to rapidly traverse interstellar distances.
If alien craft are visiting the Earth they must be traveling through wormholes or some similar method.
A wormhole requires a device at each end to keep the wormhole open, so no - that's no way to travel to new places. But it might be a very useful way to make an expressway between two points that one would frequently like to visit.
In a sense, gravitational field propulsion is a means of "burrowing through spacetime," so it's basically as good as a wormhole. And much easier to build.
Because they are constantly coming and going through these doorways, they are rarely exposed to us visually.
But we don't see that happening - people see these craft moving very quickly from one place to another, not "jumping" through "doorways." And thousands of people see these craft every year. In my view, they appear to be gravitational field propulsion devices because that's exactly what they are - the predicted performance characteristics match the observations *perfectly*.