The second "Sound" is almost exactly what a starter whose "Bendix"
won't engage sounds like.
[Starter spins with NO LOAD,since it doesn't engage]
The fact that it happens during the "Glow" portion of the ignition sequence
says Zomething is amiss with the Wiring,since that's an Impossibility.
Either the ELECTRICAL portion of the Ignition Switch is at fault.
OR ZOMEBODY'S Buggered up your Starter's Wiring.

OR Mayhaps BOTH ?

"Shorting" a Starter has risks and I hope you've not found a different
type of one !

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'84 300SD sold
124.128