Spotlight search doesn't work on Time Machine after Lion

I've got a new (couple of months old) iMac that came with Snow Leopard. Since updating to Lion however, I've been unable to search for any files on my Time Machine drive (external USB connected HDD).

I've tried forcing Spotlight to re-index my external drive by adding the external drive to the Spotlight Privacy and then removing again but I'm not convinced It's doing anything. I've also tried repairing the time machine disk in Disk Utility (which completed with no problems)

The strange thing about this problem is that if I set Finder to show all hidden files (via the "defaults write com.apple.finder AppleShowAllFiles TRUE" command), after I reboot and go into Time Machine, it starts picking up files that I'm searching for. But when I disable the hidden files again, Spotlight goes back to returning 0 results.

This is really frustrating as everything was working before I updated to Lion. I've tried searching for other clues to clearing my Spotlight cache on the external drive but nothing has worked. Some methods (such as this:- http://web.me.com/pondini/Time_Machine/A5.html) refer to repairing a sparse bundle on my external drive but I can't find the file it's talking about. Am I missing something obvious here?

Any help would be most appreciated.