What's broke?
I don't hear it when driving. I hear it ONLY sitting..in neutral...clutch pedal not pushed.
Since you mentioned the engine vibrating, I gotta tell ya:
running and sittin in Neutral the clutch is spinning with the engine, and so is the transmission Input gear, and the cluster and every gear on the mainshaft. Only the synchronizers are stationary on the stationary mainshaft.
Stay with me now;
If the engine is the source of the vibration, it often happens that said vibration causes the cluster to rattle amongst the gears and specifically against the Input gear.
Therefore, I would look to the engine FIRST before dropping the trans.
The most common thing to cause a vibration of the type you describe, would be a contaminant in the fuel.
The second most common thing would be debris in the idle bleeds.
The Third would be a vacuum leak, as what happens when a cap falls off a port.
Other sources would be a camlobe going down, over-advanced ignition timing, or a compression problem in one hole, as when the headgasket lets go.
I think I would at least check the engine first ,.............