In Inductive Position Sensor the air gap between the metal target and coil changes the position value?
You can find lots of theory if you look for resolver. It's the same principle, then you'll understand that if you divide two secondary signals the amplitude doesn't matter, since both are weakened with same magnitude.

$$V_{sec_{sin}} = K\cdot V_{prim}\cdot sin\varphi$$
$$V_{sec_{cos}} = K\cdot V_{prim}\cdot cos\varphi$$
$$tg\varphi = \dfrac{K\cdot V_{prim}\cdot sin\varphi}{K\cdot V_{prim}\cdot cos\varphi} $$
$$V_{prim} = V_{exc}\cdot sin\omega t$$
$$tg\varphi = \dfrac{K\cdot V_{exc}\cdot sin\omega t\cdot sin\varphi}{K\cdot V_{exc}\cdot sin\omega t\cdot cos\varphi} = \dfrac{ sin\varphi}{cos\varphi}$$

Theoretically the coupling factor K and voltage amplitude has no influence, practically it has since the AD converter has a working range.