The vibration you feel are the brake hold support bearings, in the axles. These are curved pieces of plastic that will vibrate and/or groan if not lubricated or are worn out.

There are grease fittings next to these that you can try to pump some grease into; if the bearings are not worn out they they will stop vibrating, but you have to keep on top of this periodically. More likely these are worn out and probably need replacing. It's not a major job, but tough enough.

You can get a modern version with Teflon shims from Star Motors, at www.300sel.com

This is a very common issue with 6.3s, by the way. 90%+ of them have it at one time or another.

Cheers,
Gerry