I've never suffered a partial tricep tear, but I have suffered a partial bicep tear (about 10 years ago).
Lots of bruising, and basically did nothing with it for about 4 weeks. The started doing extremely light dumbbell work (like 5lb dumbbells). Just getting some blood flow to the muscle really helped the healing process, but I 'm still glad I didn't start working that muscle too soon. Better to take it slow and steady.