Looking at the video, realized that the EM WAVES are in phase, so Electric and Magnetic, at any one point you choose, are both oscillating in phase. So the peak strengths both at same time.
I almost think, by now, this needs a voting system...
But my take is:
Looking at one point, say, on a COAX cable, there are times, when there is no field, as SINE shaped wave vibrates down the wire. Opposite to that, there are times when there is no current, in the wire.
In my view, any current, time varying, produces the magnetic field, expands around the coax, or other configured cable, like twisted pair. So it's both, outside wire, by fields moving, and in the wire, during times the electrons move. Electrons are moving in little back and forth oscillations, so there is a time (instant) when current is zero, ... then it reverses direction.
So both parameters are 'not' there, at certain instants, but the whole SINE wave is definitely there, moving past your vantage point. Moving as a current, in the wire, that's going to be the FORCE, of the current, not an electron mass pushing or anything; actual electron current is very slow, relatively.
And then, also, the energy, for doing work, moves outside the wire too. In fact, it's that moving field, in my opinion, that continually renews the wire's internal field and resulting current. Same thing the other way; sometimes the external fields are zero, and they get renewed, by the wire's current.
All relates to that old idiom, about a lion chasing its tail. Both processes renew each other, in turn, going down the transmission line, or when considering one point in the line.
Like I said: sometimes there is no field, but soon there will be, (as the SINE shaped wave builds back up).