There are some confusing things to ponder when figuring how fast electricity is going down the copper wires of our daily lives. From a light switch to bulb, it seems the speed of light might be the answer. There is more to it though and it requires some clarification of what is going on with electricity.
Electricity is an ambiguous word which typically is referring to current. Current is often said to be “flowing electrons”. This here is a misrepresentation. The electrons are not flowing down the wire in any reasonable sense. What is flowing down the wire is electric force (i.e. charge). If a wire has a voltage this means there is a difference of charge from one end to the other and so a potential energy. If the wire is an electrical conductor (has a charge, basically unbalanced protons to electrons) it will carry the electric force proportionally to the voltage. This force can translate to current (e.g. amps) and is basically how much the electrons are being displaced within the atom, which will determine charge, and the energy released when it is balanced. Electric force is propagated as electromagnetic waves and will likewise go the speed of light (a.k.a. “c”). Note: electric and magnetic force are fundamentally derived from EM force.
This suggests the electrons themselves are moving in a much different way than the “flow of electrons” view. The electrons are strongly bound to the atom and so tend to stay with their atom despite the electric force running through. An estimated average electron speed in atomic orbit is millions of mph (let’s say 20-60% c). Occasionally, a chance energy flux can excite an electron away from an atom into another, but no flow occurs since it could fly off the opposite direction of the current and it is in no harmony or consistent rate with other electrons to be a flow; so this is just electron drift. What is critical is that the electrons are offset by the energy applied to the wire and the offset is electric force, leaving the electron cloud distorted but not necessarily moving much faster. So the speed of electricity as current would be c. Measured over the whole wire, electricity is a bit less than c as he EM waves interchange between atoms.
This would mean that electricity as we think of it is electromagnetic waves moving through a medium of electrons. Just as in a body of water with displacement(energy) moving along as a wave, the water moves only a bit as it passes a bump from one to the other; or likewise, sound speeding through slow air. Likewise, electrons are bumped which forms an imbalance of charge, which when adjusted by the protons in the nucleus is dissipated away from the atom as electromagnetic energy on to the next atom, with the direction is maintained as the voltage is maintained. This is why copper ions (Cu+2), with two more protons than electrons, make such good wiring; when electrons from one are crammed into the neighbor it makes for a great medium to transfer EM energy.