Okay, I have no idea how one looks like, and what are the chances of finding one in a continuous game. Please advise. Cheers.
I usually happen to find them on missions involving the seeking lights, when you have to find some items on the ocean floor. As soon as I receive the lights, I let the submarine dive and activate the searching light. Then I travel to the location where I have to collect the items for the quest.
On the way, it is possible to stumble upon the sites by accident.
Of course, you can systematically search for the sites when you have got the searchlights if you do not care about the actual quest. They will stay active as long as the quest is active.
In a continuous game there will always spawn three abandoned facilities on the small underwater islands (the ones you cannot settle). If your (submerged) submarine happens to pass one, on purpose or by accident, a notification pops up.
You do not require searchlights in order to find these sites, they are available at any time to claim prototypes, but only once per site.
Also, the NPC Hiro Ebashi offers a diplomatic action called technology scanner, which will reveal up to three new sites for you to claim. This can be repeated indefinetly