My new to me '99 Road King Classic has pretty solid shake at idle. It smooths right out when the engine revs, and its not unbearable or anything, its just considerably more than my friend's '05 RKC with the same engine.

What is the likely source of this vibration? I'm thinking one of the rubber mounts? Can this job be done by me?

Also noticed a very small drip of oil, appeared to come from a bolt under the engine on the horn side of the bottom. Is there a separate drain plug for the primary chaincase? I will try just cleaning it up and making sure the bolt is tight.

 

Is your bike a fi or carb, and yes under the big round derby cover there is a drain plug for the primary, you fill it up thru the inspection cover, small cover in front of the derby cover. Go out and buy the manual from HD, it will tell you everything you need to know and answer all your questions.

 

As far as the engine shake at idle goes I would check the front motor mount, my guess is it needs to be changed.

 

I had a 99. Don't know about your engine shake, probably motor mount. Watch tightening that primary plug to tight. On a 99 that's a tapered pipe plug. You could crack the case. And if that oil drip is coming from the left front of your bike, it could be where the stator wires come out of the case. Mine leaked there. For what ever it's worth. And a manual will pay for it's self over and over.

 

Maybe the 99 shakes a bit more than the 05. My 13 shakes a lot less than the 05 did. But yes, check the front motor mount.
The leak may not be coming for the primary bolt. Could also be from the back of the primary. Everything will seep to the lowest point on the bike.