Disable Spotlight search in Time Machine backup

I'm running Mac OS X 10.7 Lion and am trying to disable Spotlight indexing on my Time Machine hard drive, as the mds and mdworker processes are running wildly through all day at 15-60% of CPU...

What bugs me is not that my MacBook is running slowly but that this CPU consumption kills some cycles of my battery through time just for a wasting-never-used search in my Time Machine backup...

I've tried to add the Backups.backupdb folder from the Time Machine HD to the Privacy list, but I get this message:

“Backups.backupdb” is a Time Machine backup folder. You cannot add it to the privacy list.

I then tried to completely stop Spotlight using sudo mdutil -a -i off; this is the output:

/:
    Indexing disabled.
/.MobileBackups:
    Indexing enabled. 
/Volumes/Files:
    Indexing and searching disabled.
/Volumes/Komodo-Edit-6:
    Indexing disabled.
/Volumes/MobileBackups:
    Index is read-only.
/Volumes/MobileBackups/Backups.backupdb:
    Index is read-only.
/Volumes/TimeMachine:
    Indexing and searching disabled.
/Volumes/TimeMachine/Backups.backupdb:
    Indexing enabled.

How can I disable this annoying Spotlight behavior? I don't use it very much and it would be painless to disable it for good, or at least stop indexing my Time Machine backup...

Solution 1:

Most likely it is not possible

From Spotless's (An OSX app which helps disable Spotlight indexing) change log:

We also added support of Time Machine backup volumes. 
Since these volumes cannot have their indexing disabled permanently, 
Spotless no longer attempts to modify them.

So it looks like even programmatically you can not disable Spotlight from indexing Time Machine.

Solution 2:

I finally found you cannot disable Spotlight to index Backups.backupdb.

Apple Support. OS X El Capitan: Spotlight preferences

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.