Where did Radagast dwell?

[Legate of Amon Lanc]

Well, yes, this idea would be possible as well. In that case, Radagast's movement to South would be probably a movement made by the White Council in their preparations to strike towards Dol Guldur, planting a scout near the targeted spot.

But I think we have said quite enough on that topic. Now, we can make a nice bridge to my next question: it seems obvious, and it has been already mentioned here, that Radagast abandoned his dwelling later. The fact that the scouting party did not find him is not much of a proof of that; he could have been just outside for a few days or weeks, let's say rallying some birds to his cause in sending help to Gandalf or Saruman. But from Gandalf's words at the Council:

It was Radagast the Brown, who at one time dwelt at Rhosgobel, near the borders of Mirkwood.

we can presume that Radagast had, for some reason, indeed left his home. Of course we could interpretate it that way that he first (i.e. when he came to Middle-Earth) did not have any "home" and later he settled down at Rhosgobel, but all the other things could point to the fact that he was indeed living there and then, some time after the events described in the Hobbit, he left his home. Now, taking aside my and Aiwendil's hypothesis about "two homes", where else and why do you think Radagast could move away from his home? I would be very interested to hear different ideas and suggestions, for many people can bring many different and interesting ideas. So, what do you think? Why did Radagast leave Rhosgobel (if he did) and where did he go (if anywhere)?