Time Machine with external drives connected to server

my solution to this issue is simply to use Finder on the machine to be backed up, mount the shared backup drive(s) manually, then tell Time Machine to 'back up now'.

No drama.

The long detailed way:

Finder > File > New Window

Select a sidebar item such as YourMacName to show top-level of the machine, which should show YourMacName, your external drive names, and and 'Network'. Double-click Network.

This should show YourServer, and any other possible File server devices such as other Macs or PCs on your local network.

Double-click YourServer, and it will try to connect (and may fail) showing a screen like this:

use the 'connect as' button. this opens a login and connect dialog. Enter a username and password that has the right to read and write the files you want On the SERVER computer. "Guest" will be inadequate because it does not have the popper rights for files you need.

select the Folders you would like Mounted (as if they were local Volumes) from the list that appears

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The "cut to the chase" way:

Finder > Go > Connect to Server

you may have to (Browse) to find the server

the login to server dialog opens, similar to before

your initial post suggested you had ALREADT assigned these drives as the backup drives, and had subsequently received an error message that the drives were not available.

to make them available agin, you use the procedure I posted.

if you have torn them out, you WILL have to re-establish them as THE backup drives, actually as the 'remote backup destination'. Once properly designated, Time Machine will remember them forever (unless you intervene). Whether it can actually back up to them is the subject of our discussions.

Then you click the Time Machine icon on the menubar and choose "back up now" ... and away it goes.

if you did not solve the problem, you get an error message instead.