If signamancy is form equals function. Then a signamancer might just be able to change the form, and therefore the function of a unit or item. Temporarily turn a light unit into a heavy. Or maybe use all juice to turn an enemy unit into a sheep.
We already know that style of casting (adding/subtracting specials) is Weirdomancy.
Think about it in a more physical sense. Signamancer plants sign that says, "Stay off the grass," "No hippies need apply."... or in Erfworld terms, "No infantry permitted here," "Only heavies allowed to attack." Their signs can create restrictions and permissions contrary to normal rules. A good general can use such restrictions to gain tactical and strategic advantage.
If FAQ was to evacuate preemptively, why take all casters in the first place?
Depends on whether you are completely abandoning the idea of staying. If you are not, then yes, leave some behind. If you are completely abandoning, then don't.
Because that would be a big risk, for several reasons:
Overstating "big" there by a lot.
To be guaranteed of taking the enemy capital, they're going to need every resource they can bring to bear.
There's a big assumption there. You're assuming the enemy has significant defenses. In the rock-paper-scissors world of combat having the correct offense can minimize defenses, and bringing extra resources that are vulnerable to the defenses creates loss where there would otherwise be none.
Leaving ANY infantry behind, and 3 of their casters (all of whom have proven or speculative combat applications that are very powerful) will jeopardize that chance, and nothing would be worse than evacuating, losing, and being stranded in hostile territory.
Case in point, Goodminton. Bringing infantry to an air fight is a waste.
Because they lack a Thinkamancer, the city might fall without warning. The evacuees would suddenly lose that treasury, and have nothing to create a new city with or pay upkeep.
The assumption is that the attackers take as much of the treasury as possible, the moneymancer converts to gems that can be carried into the MK, and so the treasury leaves with the casters.
Sacking a city yields a huge amount of schmuckers. They may NEED to sack their own cities as they leave and get those schmuckers for the plan to work.
We don't know that it is "huge". And if the treasury is already too large to carry, extra is wasted.
Whoever finds them would realize that they didn't find the Ruler, and would thus know the side still exists,
So what? Going to bust your plan in order to hunt down a newly created Side? If they flee, that means fewer losses now for the attackers. For Haffaton and its generally peaceable methods, this is a bonus. And they left cover the moment they left FAQ. Banhammer is not going to find another bubble side location, so he's out in the real world.