Cant see any comments at all just a picture of a lamp in a holder accompanied by annoying music. Could be almost anything - lamp in series with fan or another light fitting used to be a classic with decorators making a mess of loop through rose (aka 3 plate) ceiling fittings. I suspect that the use of phones to take a before and after pic have reduced this a bit

Equally could be an LED 'filament' lamp and as above capacitance.

I agree, shower  induced voltage drop is likely spurious.

Mike

Thank you. That is an LED lamp.

That is an LED lamp.

agreed - e.g. https://www.toolstation.com/sylvania-led-rt-a60-filament-clear-gls-lamp/p85671

Real filament (incandescent) GLS lamps (at least of the ordinary domestic type) generally had the filament as a flat semicircle at towards the top held up on a number of fine wires from a central glass post (or as an obvious coil in much older ones) - like this one https://www.easy-lightbulbs.com/products/gls-100w-b22d-bc-240v-philips-clear-light-bulb . The 'sticks' are LEDs trying to look like filaments.

We're likely back to the capacitive coupling theory.

   - Andy.

Okay so you reckon that the light is gaining an induced voltage from the shower circuit caused by capacitive coupling. Would this effect be increased with a higher voltage drop? 

we lose a further 5 volts which goes down to earth and the neutral conductor. 

Erm, voltage is probably best thought of as a pressure difference between two points - volts don't travel as such. It's the current (amps) that flows - and flowing along something with resistance (which everything has) results in the pressure drop (voltage difference). Text book wise it's all just Ohm's Law. V=IR. You've got the same current flowing through all parts of this simple circuit - the overall current is regulated by  the overall resistance of the circuit (load and all the connecting wires) and the supply  voltage as a result is divided up across each component of the circuit - so the voltage of across each part in series adds up to the original supply  voltage. There's nothing special about the N conductor in this regard - it carries current and has a voltage difference along its length in exactly the same way as the line conductor.

   - Andy.