Honda Harmony II transmission/clutch
My HRB216TDA has developed the same problem, and furthermore seemed to not declutch completely. I've opened up the transmission today and found not a drop of oil. The clutch mechanism is a dual-cone pressure type. There is no spring to ensure positive disengagement, so oil is a must. Removing the transmission is a bit of a chore, and separating the case halves requires a razor blade to break the silicone sealant.
The rear wheels each have a ratchet mechanism. I'm not sure, but I assume these are to allow the lawnmower to be pushed forward without forcing the axle and gears to rotate as well. But when the mower is pulled backwards, these ratchets grab and will rotate the axle. Provided the clutch is disengaged, the wheels will turn. Otherwise the wheels will drag. If you do take apart the ratchets to clean and lube, you'll find each has a metal key with a small spring recessed into the axle.
This spring when the rig wouldn't start, I did the usual carburator cleanup, but the engine would run for only 10 seconds before dying. My wife says "change the spark plug". Well, the plug looked ok to me, so the carburator came off twice more for cleaning, with the same result. Frustrated, I installed a new spark plug. Problem solved
. Always listen to your wife