The 0 movement idea is connected to their status as guardians. They are assigned to guard one special point and thus stay there until attackers arrive. Teleporting just means you assign them another place they should guard. Gargoyles were terrifying statues on the top of cathedrals. They were said to protect them from evil so IMHO it makes sense making them into guardians that don't leave their place until an intruder is nearby.
You could create a building that mirrors citadel of light:
Ancient Tower 240
If an enemy enters a tile adjectant to the city a gargoyle with 3 duration is spawned.
Instead of creating new buildings you could say that all wall buildings gain this ability once you have researched Engineering (i.e. walls, palisades and perhaps Wall of Stone.) Another idea would be to let their fort-Castle-citadel improvement line spawn gargoyles once they have Engineering.
But as I already said you could just make them into a longbowarcher with mithril that can't be promoted. Then it would be nothing "special" but at least it would be as strong as any other golem.
You could create a building that mirrors citadel of light:
Ancient Tower 240

If an enemy enters a tile adjectant to the city a gargoyle with 3 duration is spawned.
Instead of creating new buildings you could say that all wall buildings gain this ability once you have researched Engineering (i.e. walls, palisades and perhaps Wall of Stone.) Another idea would be to let their fort-Castle-citadel improvement line spawn gargoyles once they have Engineering.
But as I already said you could just make them into a longbowarcher with mithril that can't be promoted. Then it would be nothing "special" but at least it would be as strong as any other golem.