"A 60 Hz sine wave has a wavelength of 5000 kilometers. "

Actually, it's not quite that. The speed of electrical conduction in conventional systems is about .6c usually. This brings the wavelength down to 3000 km. I'd suspect that the various inductive and capacitive elements (like transformers) that are usually between the source and sink would unsync two light sources across a city grid.

It doesn't really matter because the plasma in the tube stays hot too long. The silica or quartz capsule holding the Na plasma will be very hot after a short period as well.

If i'm not mistaken, the value of sodium lights is not the delightful orange glow (ha ha..) but that they emit most (if not all?) of their energy in discrete (thermally broadened) visible wavelengths. This limits the plasma's ability to radiatively cool and so it stays hot longer.

The fact that it's a sine wave doesn't help you much either, the plasma once ionized is a conductive path an will experience some ohmic heating for all but an infintecimal of the cycle.

I'll still check around to see if I can borrow a suitable photodiode and scope to try to make a measurement.