Rest as long as it takes for the pain to go away.
You can do stuff if it gives you no pain. Recognize, though, that it may start hurting and you will want to stop. Never do anything on pain.
Massage, hydrate well, stretch the area. Sometimes joint/connective tissue stuff can help like glucosamine & condroitin, fish oil, shark, etc.
Eccentrics... ehh. Eccentrics can cause tendonitis. It may help or it might not. If it causes pain don't do it. I would just recommend going back into workouts lightly.
P.S. read some other threads on this forum.