Does Detect Magic make an Arcane Mark placed on an invisible surface glow?

Invisible arcane marks glow when hit by Detect Magic.

Usually, how this works is that someone casts Detect Magic on an item and they see this fluorescent drawing on it, marking it as the belonging of some specific mage.

This time, however, we have a creature that likes turning invisible every time it hears our magus cast True Strike or every time too many people swarm them, and the magus would like to slap an arcane mark on their back so that, when the creature goes invisible, a round 1 Detect Magic causes the glow, marking the square and letting everyone but the Detect Magic caster target the right square.

Does this work?