notice that emi filters work well if you have complete wiring, F, N,GND (phase, null and ground -single-phase power supply installation of a house-) if you have only F and N and no GND, only differential noises (currents) will be filtered common mode noises not (), anyway that filter should make a difference if your neon light is producing that noise. Personally i would not buy that filter (it is not a big deal, it's just a LC filter, coil and capacitor in a little box ;-) ) , i would make a test with a home built filter ....
(to make a coil take 2 intertwined wires (F and N) and wound them on a ferrite rod, about 10-20 turns. In addition to one end of the coil put any capacitor between F and the N, you can find with ~250 Vac. nominal voltage rating . Insert the assembly between the neon light and power supply and see if there is any effect.....
... or try to put only a capacitor in parallel to your neon light's power supply terminal -between F and N- and see if there is any effect )
PS : is your neon light in a classical configuration with starter & coil, or is it with electronic ballast ?
(the classic scheme produces noise only at start-up (while starter and coil makes the ionization of gas in the tube, called 'ignition' of the tube ........) and the electronic ballast produces noise continuously since basically it's a switch mode power supply .... )
2. PS: take care when working at at ac mains, remove the voltage from the installation you are working by disconnecting the appropriate fuse at main panel, if you are not shore about which fuse disconnect's your circuit, then disconnect all fuses