Why bother to fire grill mussels?
What do you gain from grilling mussels? If you're grilling them on the BBQ like the picture below, all the mussel fluid will drip into the BBQ or evaporate.
Perhaps I'm just lazy, but I see no point to dirtying then cleaning up the BBQ, when you can just steam mussels in a Dutch oven or rondeau on a cook top.
Linda Duncan, Mussels: Preparing, Cooking and Enjoying a Sensational Seafood, p 147.