In neutral the drive shaft and a small part of the transmission is active, most of the rest is not moving, and the rest is turning at the engine speed. Putting the clutch in (should have suggested that too) will stop that part too. I think your transmission is at fault.

If you do take it out, change the clutch.

A story with a happy ending:
My wifes old Datsun had its oil leak out cause the case bolts had loosened. I re-filled it and tightened the bolts but it had devoloped a "sound." Then a couple of years later it started making real expensive sounds. When I took the drain plug out chunks of metal came out

It turns out it was the soft metal of a bearing cage that came apart and got chewed up by the gears. All I had to do was floss the teeth they didn't seem to mind the bearing cage, and replace the bearing, dealer part, for all of $15

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5 speed '91 190E 2.6 320,000 mi. (new car, fast, smooth as silk six, couldn't find any more Peugeots)
5 speed '85 Peugeot 505 2.5l Turbo Diesel 266,000 mi. (old car, fast for a diesel, had 2 others)
5 speed '01 Jetta V6 (new wifes car, pretty quick)
5 speed '85 Peugeot 505 2.2l Turbo Gas 197,000 mi. (wifes car, faster, sadly gone just short of 200k )
5 speed '83 Yamaha 750 Maxim 14,000 mi. (fastest)
0 speed 4' x 8' 1800 lb Harbor Freight utility trailer (only as fast as what's pulling it)