Inspire excellence shares timer with Inspire courage and using any of them puts the other on a 30 cool down timer. Note that Inspire courage is normally on a 10 second timer when sung.
Inspire courage also doesn't stack with Exceptional +1 gear. Intended or a bug? Fighters got their stance bonuses changed to stack with the exceptional +2 gear change so I'm guessing this is a bug/not intended but confirmation would be nice.