Why does the amount of my mouthwash influence the colour?

This may be a phenomenon due to Beer's Law: the amount of light a material absorbs is related to the path length of the light.

Since we're looking at the liquid from above the one on the left is a length of, say, 2cm ....whereas the one on the right is a path length of, let's say, 15cm.

Since the light is traveling through a much shorter length when it's empty than when it's full the color appears lighter.... i.e. less light is absorbed.

Of course I can't see if this is the case from the picture. Try looking at the two solutions through the length... if they're the same darkness then it's a Beer's. If they're still different then something else is going on. (But I'm betting on it being Beer's.)