Signs point to “yes” with some wiggle room for GM interpretation.
The first hurdle: can Arcane Mark be cast on a creature?
If an arcane mark is placed on a living being, …
The second hurdle: can it be cast on an unwilling creature?
… and, there’s no “Target” field, so the spell doesn’t specify that it can’t be cast on an unwilling creature (though, a touch attack is likely required to do so).
The third hurdle: does it matter how the Mark is made invisible?
An Arcane Mark itself “can be visible or invisible”, and “(i)f an invisible mark is made, a detect magic spell causes it to glow and be visible”. So, an Arcane Mark which is created as an invisible Mark is definitely revealed by Detect Magic. But, what about a mark which is made on something which is later affected by Invisibility (or its variants)?
Fortunately, Invisibility answers that question:
Light, however, never becomes invisible, although a source of light can become so (thus, the effect is that of a light with no visible source).
Since the Arcane Mark explicitly glows, it’s a light source; since it’s a light source, the mark itself is visible-ish (at the very least, the square it’s in should be readily detectible, in the general case).
So, where does GM interpretation come in?
First: since Arcane Mark doesn’t explicitly state that it can be cast on an unwilling target, the GM could rule that it can’t be. This is something that the GM should be freely willing to talk about before the tactic is tried, of course.
Second: if the Mark is somewhere that the target can cover it (with a cloak or something), the GM could rule that the target can cover the mark, hiding the light (this GM remembers this being a valid option, but can’t find rules support at the moment; also, in fairness, this rule should apply to light sources generally: players should be able to close an invisible bullseye lantern or hide an everburning torch in their cloak to prevent foes from seeing the light source at the cost of not having it available themselves).
Third: the GM could rule that the area is bright enough that determining which square the target is in requires a perception check (simulationist real-world example: telling if a non-OLED LCD/LED display is on by seeing the … “brighter shade of black”, I guess … in a bright room vs. a dark room).
For what it’s worth, this GM thinks the tactic is clever. Further, since there’s a real cost to using it (it burns an action, which is the most valuable currency in the game), I wouldn’t be prone to nerfing it via either of the “interpretation” options above. However, I would have some canny foes who have had time and reason to watch the PCs in action (or to have received reports) use the tactic against them or be otherwise prepared for it (eg., by preparing – and preparing for – Darkness).