The Scarlet Guard's motto is wholly appropriate for a number of reasons. First and foremost, this resistance movement's dedicated to rising up against the Silver nobles in their fight for justice and equality. So the Scarlet Guard is determined to rise up just like the dawn. Also, red is a color traditionally associated with revolutionary or radical political movements. The Scarlet Guard definitely falls into this category as its avowed aim is to overthrow the cruel, tyrannical regime of King Tiberias. It doesn't get much more radical or revolutionary than that.
But The Scarlet Guard wants to do so much more than just destroy an old order; it wants to build a new one, too. The foot soldiers of the rebellion such as Elara and Maven want to usher in a bright new dawn of freedom and equality. So once again we can see why The Scarlet Guard's motto is well-chosen: like the dawn, it will rise, it will be red, and it will herald the arrival of a new day.