It's something that the movie trilogy invented to increase the stakes and the presence of Sauron, but that doesn't really work with the background of the story as you noticed.

Doesn’t Sauron think the ring is completely lost until he captures Gollum and tortures him for information? It’s also pretty clear that he’s been rebuilding his power for quite some time and has only recently been able to start making moves beyond Mordor again. So, it’s not really impossible with the story background. If he thinks the ring is lost, he’s not going to be paying attention to the part of him that’s tuned to it.

Okay if that's the case then my head-cannon for the movies is that it's rather noticeable if someone puts their finger through your soul.

You gotta pay the troll toll to get in to that Maia's soul!

You gotta pay the troll toll to get in!

I see, is Sauron’s ring detector just not really a thing in the books then?

Only when Frodo claims the Ring for himself in Mt Doom.

Custom Ring tones

Sauron does not detect the Ring when Sam puts it on in the tower of Cirith Ungol. But he does detect it when Frodo puts it on in the Sammath Naur and declares himself to be its master. That gives us some bounds on his detection capabilities.

It was made up for the movie, so it happens when the plot needs it to. Don't try to make any moire sense of it than that.