Wouldn't an indicator for "autopilot processing in progress" be nice?

I have been looking for a way of knowing that the game is doing the autopilot moves so I don't go punching the daylights out of the "find" button (no, I really don't, but it is tempting). I noticed when the hourglass was added to the game for placement over the "turn" button when the game was doing the "next turn" processing, and thought it a great idea. I think putting the houglass icon over the "find" button when the game is processing the autopilot moves would be an ideal indicator.