What sort of sensors are used for sensing the positions of the control surfaces for the ECAM F/CTL page on Airbus aircraft?
No, they are not proximity switches, which are suitable olny to detect when a moving part has reached one of few predetermined positions (as in a landing gear, in which only two predetermined positions – up and down – are of interest; any other intermediate position is transient and undesirable).

For those moving parts that are required to be positioned anywhere within a given range, such as the control surfaces of an aircraft, you need a sensor (aka transducer) that can accurately measure the position of the part at any point within that range, not just at the ends. As already mentioned, the device of choice is the linear variable differential transformer (LVDT), or its rotary variant RVDT.

For example, this is the schematic of a yaw damper servo actuator of an Airbus A320:



Element No. 4 is an LVDT that measures the displacement of the actuating rod attached to the rudder. Similar devices are used for ailerons and elevators. The elevators also have an additional RVDT fitted directly onto the elevator's torque tube, in addition to the LVDT part of the servo control.