Should it not work both ways? i.e. If when Sauron put on the One Ring, and the other ring bearers became instantly aware of him, would then not Sauron instantly be aware of them too and know exactly who they were?

It doesn't make sense that only the Elven ring bearers were aware of Sauron when he put the One Ring on, while he was not aware of them. I think this is a problem in the text that is not fully explained by Tolkien. I think it has to work both ways, in which case when Sauron put his One Ring on he was instantly aware of who had the Elven rings, if they were wearing them at that instant.

At the time it seems Galadriel had one and Gil-Galad the other two, so Sauron must have known. Also, we can assume that when Gil-galad assaulted Barad Dur with Cirdan, they each had their rings on in order to use their power (the red ring kindled the hearts of those around it to courage, the blue ring it is not said what it does), as did Sauron, so at that point Sauron would have known that Gil-galad had the blue ring and Cirdan the red ring.

This is what I think is going on really. So long as the elves wear their rings and Sauron his, they all are aware of each other. Another important thing to support this is that Frodo, when he puts on the One Ring in Amon Hen, hears a voice telling him to take it off. This I believe is the voice of Gandalf communicating through the red ring to Frodo. However, Frodo cannot communicate back to Gandalf because he is not powerful enough when wearing the One Ring. Or perhaps this is proof that the communication is indeed only one way, the Elven rings are aware of the One and not the one of the other three? Perhaps this is the true explanation of what it means "the three were hidden from Sauron". Interesting.

Should it not work both ways? i.e. If when Sauron put on the One Ring, and the other ring bearers became instantly aware of him, would then not Sauron instantly be aware of them too and know exactly who they were?

It doesn't make sense that only the Elven ring bearers were aware of Sauron when he put the One Ring on, while he was not aware of them. I think this is a problem in the text that is not fully explained by Tolkien. I think it has to work both ways, in which case when Sauron put his One Ring on he was instantly aware of who had the Elven rings, if they were wearing them at that instant.

At the time it seems Galadriel had one and Gil-galad the other two, so Sauron must have known. Also, we can assume that when Gil-galad assaulted Barad-dûr with Círdan, they each had their rings on in order to use their power (the red ring kindled the hearts of those around it to courage, the blue ring it is not said what it does), as did Sauron, so at that point Sauron would have known that Gil-galad had the blue ring and Círdan the red ring.

This is what I think is going on really. So long as the elves wear their rings and Sauron his, they all are aware of each other. Another important thing to support this is that Frodo, when he puts on the One Ring in Amon Hen, hears a voice telling him to take it off. This I believe is the voice of Gandalf communicating through the red ring to Frodo. However, Frodo cannot communicate back to Gandalf because he is not powerful enough when wearing the One Ring. Or perhaps this is proof that the communication is indeed only one way, the Elven rings are aware of the One and not the one of the other three? Perhaps this is the true explanation of what it means "the three were hidden from Sauron". Interesting.

Should it not work both ways? If when Sauron put on the one ring, and the other ring bearers became instantly aware of him, would then not Sauron instantly be aware of THEM too and know exactly who they were? It doesn't make sense that only the elven ring bearers were aware of Sauron when he put the one ring on, but he was not aware of them. I think this is a problem in the text that is not fully explained by Tolkien. I think it has to work both ways, in which case when Sauron put his one ring on he was instantly aware of who had the elven rings, if they were wearing them at that instant. At the time it seems Galadriel had one and Gil-Galad the other two, so Sauron must have known. Also, we can assume that when Gil-galad assaulted Barad Dur with Cirdan, they each had their rings on in order to use their power (the red ring kindled the hearts of those around it to courage, the blue ring it is not said what it does), as did Sauron, so at that point Sauron would have known that Gilgalad had the blue ring and Cirdan the red ring. This is what I think is going on really. So long as the elves wear their rings and Sauron his, they all are aware of each other. Another important thing to support this is that Frodo, when he puts on the one ring in Amon Hen, he hears a voice telling him to take it off. This I believe is the voice of Gandalf communicating through the red ring to Frodo. However, Frodo cannot communicate back to Gandalf because he is not powerful enough when wearing the one ring. Or perhaps this is proof that the communication is indeed only one way, the elven rings are aware of the One and not the one of the other three? Perhaps this is the true explanation of what it means "the three were hidden from Sauron". Interesting.

Should it not work both ways? i.e. If when Sauron put on the One Ring, and the other ring bearers became instantly aware of him, would then not Sauron instantly be aware of them too and know exactly who they were? 

It doesn't make sense that only the Elven ring bearers were aware of Sauron when he put the One Ring on, while he was not aware of them. I think this is a problem in the text that is not fully explained by Tolkien. I think it has to work both ways, in which case when Sauron put his One Ring on he was instantly aware of who had the Elven rings, if they were wearing them at that instant. 

At the time it seems Galadriel had one and Gil-Galad the other two, so Sauron must have known. Also, we can assume that when Gil-galad assaulted Barad Dur with Cirdan, they each had their rings on in order to use their power (the red ring kindled the hearts of those around it to courage, the blue ring it is not said what it does), as did Sauron, so at that point Sauron would have known that Gil-galad had the blue ring and Cirdan the red ring. 

This is what I think is going on really. So long as the elves wear their rings and Sauron his, they all are aware of each other. Another important thing to support this is that Frodo, when he puts on the One Ring in Amon Hen, hears a voice telling him to take it off. This I believe is the voice of Gandalf communicating through the red ring to Frodo. However, Frodo cannot communicate back to Gandalf because he is not powerful enough when wearing the One Ring. Or perhaps this is proof that the communication is indeed only one way, the Elven rings are aware of the One and not the one of the other three? Perhaps this is the true explanation of what it means "the three were hidden from Sauron". Interesting.