It's definitely electrical and it's to do with the earthing, but it is not a defect in anything. It's just the way the system works.
Earth potential is not the same at every square meter of the planet, or local area for that matter.
The electrical system is only earthed at one point for each house or switchboard.
The earth and neutral lines are joined together at the switchboard and then the earth line is taken to a single earth peg driven into the ground near a water service tap, and also connected to your copper water pipe at that point.
That is the earth reference point for your house and the whole area around your house.
When you stand in the shower, your wet feet make an excellent connection with the floor, which is earth potential at a point different than the point of the earth stake. The shower head is exactly the same potential as the earth stake because it is physically connect to the earth stake by a wire at that point and conducted to the shower head by the copper pipes, assuming the pipes are still copper pipes and not the new plastic ones.
The voltage difference is very small, maybe only a volt or two, but your head is very sensitive to that sort of thing.
The small voltage makes the muscles in your eyes pulse at the 50hz mains frequency, which makes your eyes flicker.
The effect will be more or less depending on how much the earth voltage differs between the earth point and the shower floor.
If you have small cuts on your fingers and happen to lightly touch the tap or shower head with the cut part first, you can get quite a sharp tingle.
That's because the cut bypasses the high skin resistance (around 250K ohms) and so even though the voltage is very low, the cut allows a direct path into your finger which makes the effect very noticeable.
And no,... a tin foil hat will not fix it.