This discussion seems to be solely about a locally-connected TM volume. Has anyone had any experience with making a mounted shared network TM volume invisible (or un-/mounting it via scripts)? I am referring to a drive attached to a networked Mac that another Mac (in our case a MacBook Pro) would be using as its TM target.

I had contacted TimeMachineScheduler's author (Stefan Klieme) about this but he said TMS did not handle network TM volumes but he implied that Time Machine itself mounted and un-mounted TimeCapsule drives, so though the ability was there he did not know how to access it.

In our situation, for various reasons, a TimeCapsule is not really the solution we want.

Never mind - ignore my questions.
Evidently TM automatically mounts and un-mounts the backup image as needed. It does not appear to mount the entire shared network volume you initially configure TM to use, but only the sparse image of the backup.
I had set up a shared volume TM_TEST, mounted it on a different Mac's Desktop (creatively named Mac) and configured this source Mac's TM to use it. When the backup was done I noticed TM_TEST was no longer on the source Mac's Desktop. When I kicked off a manual TM backup a plain drive named "Backup of Mac" appeared then disappeared once the backup completed.

It appears that Time Machine is brighter than I am.