After looking around the Mech Land Assault DLCs settlement eDEN Station: The Goose, I found a second button which has been speculated to exist. So what does it do and where to find it? Let's start with what it does once you press both of them. Well, I don't know. And that's because of the second part of the question, where it is. As it turns out, it's beneath the ground. But take a look for yourself:
As you can see, it's about 4 meters beneath the ground near the sphere tank. So how did I find it then? I used a camera hacking tool called Extreme Injector to detach the camera from Rico and take it everywhere I want to. I got quite lucky to find it, because it's really hard to make out from a distance. But this tool only allows me to move the camera, not Rico and in order to press it I need Rico down there. But as it turns out, it's no so complicated to get Rico below the ground. Jets, which are carried by the trains on Insula Striate, are, due to a glitch, immune to collision damage. So I fast traveled to Insula Striate, caused a few train crashes until I got one with a jet. As soon as it crashed and came to a stand, I flew off, which causes the train beneath the jet to despawn. The jet falls down and lands safely. It is not possible to pull it down using the grappler, this will cause the collision bug to not work. Also, don't use the grappling hook to enter the jet, either, same thing will happen.Now that I got my jet I entered it, flew back to eDEN Station: The Goose and took a nose dive into the ground. The jet passed right through and I jumped out before it hit the water (which is everywhere at sea level below the map). I flew back up close to the button using the Bavarium wingsuit and tried to grapple myself onto it. As I tried out before all of this, you can press buttons if you are standing on top of them, so that is what I tried, since there is no ground to stand on beneath the button. As it turns out, it's extremely hard to grapple onto the button and not fall down again or accidentally grapple through the ground and end up back on the surface. After about 2 or 3 hours I managed to land on top of it. But the game decided to push me through the ground and I ended up back on the surface. But while I was standing there for about 1 second, no option to press the button appeared. Actually, there was no animation on the button either. Pushable buttons have an animated white stripe on them, this one didn't. So maybe it's not possible to push this button at all.
I'd like to ask all of you who are interested in this, to go and try this out for yourself and see if you can press this button. Any thoughts or ideas?