My cooker switch is wired in a way that the neon indicator is always
on, whether the switch is on or off. Is this correct? (I am under the
impression that the indicator should be in sync with the switch). The
cooker is mixed-energy: gas hob and electric oven, if that matters.

Moreover, I have two wall light switches that also have neon
indicators and the indicators are always on regardless whether the
switches are on or off. They must be wired by the same electrician.
But is this correct?

Thanks, -JK.