[Rumil]

I wonder, should he have decided/been allowed to stay in Middle Earth, if he joined or helped Celeborn's new elvish realm of the Greenwood in the Fourth Age?

I imagine that Dol Guldur and the environs needed 'cleaning up' after Sauron's defeat, perhaps R aided in some way. Rhosgobel was just by the eaves of Mirkwood so at least technically Radagast might come under the area that Celeborn ruled.

I'd like to think that Radagast was forgiven for his failings, for he had never turned to evil per se, unlike Saruman. Maybe he elected to stay in ME, eventually becoming a Bombadil-ish anomaly, or hitched a lift with Gimli and Legolas on the last ship?