Turning of indexing on Time Machine Volumes Spotlight is using a lot of CPU on my computer and I am tracking down why it is a problem.
I suspect it had something to do with time machine has I have a soft correlation to leaving my time machine drive plugged with spot light continually using CPU.
So I ran this command and it reports that spotlight is indexing my TM volume:
% mdutil -s &quot;/Volumes/MBP15 Time Machine&quot;
/System/Volumes/Data/Volumes/MBP15 Time Machine:
    Indexing enabled.

How do I turn off indexing of my time machine volume without having to run the command everytime I plug in my TM disk?
I tried adding it to the privacy tab and got this error:

I also tried to add the TM back up drive directly and got this:
You can't. Spotlight is an integral part of Time Machine.
https://eclecticlight.co/2016/06/20/you-cannot-turn-off-spotlight-indexing-on-your-time-machine-backup/
As quoted there, Apple support pages used to say:
If you add a Time Machine backup disk to the privacy list, you will continue to see messages that Spotlight is indexing your backup disk. This indexing is necessary for Time Machine to function properly and can’t be disabled. Spotlight does exclude from searches any items you store on your backup disk that are not part of a Time Machine backup.
(Though they have rewritten them all for Catalina.)
So the real issue is not how to stop Spotlight from indexing, but work out why it's using so much CPU, and how to mitigate that. Sometimes, Spotlight needs to ramp up for a bit, but if it's happening more regularly, or constantly, then that might be a symptom of a problem with the backup's integrity.
Or it could just be that you're backing up thousands of small files every hour which require lots of processing, or a symptom of the drive being too full, or possibly too slow. Or something else. ;-)