Brownout?, can`t say I have ever heard this before, but I was once told by a retired HT engineer, (linesman), that when lightning strikes a pylon, instead of the massive energy release going to straight into the earth, its encouraged to jump the gap across the arc rods either side of the insulator string.

This not only protects the insulator from damage, but dissipates the energy to the already `hot` lines, however the surge protection equipment in the substations detects this, and `stalls` the supply for a second, (while it figures out how dangerous the surge could be), and if its only a short burst of energy, (as in a lightning strike), it allows the supply to continue.

Hence why you see the lights go off for a second, then back on.

... the surge protection equipment in the substations detects this, and `stalls` the supply for a second,...

There is no way anything can "detect" that surge and "disconnect from it". Before any mechanism even starts to move, the surge is way long time gone.
The only way to really suppress the surges are the parallel (to the line, in other words from the line to ground) arresters, either in the form of the "discharge fingers" around the insulators (the first line of defense; absorbs most of the lighting energy) and their faster, but less robust semiconductor (like a VDR or so) "buddy" at the substation (it is way faster in response, but can not handle as high energies, it is supposed to handle only  the first rising peak the slower "insulator finger" still passes). With all of these we are talking about response time in microseconds (the complete lighting strike takes just few 100 microseconds before it is over)
But the problem with these is, once they are ionized, they force the voltage down (that is the main reason why they are there), but then conduct the electricity as long as they are fed by the current. And because their drop uses to be lower than the operating voltage on that line, the current could be fed from the power network. This will obviously destroy them.
So in the substation this is detected (in fact it is detected as any other ground fault or an overcurrent) and that line is temporarily disconnected from the power for some second or so and then connected back to restore the service. This happens way after the overvoltage event, but the aim is not to stop any overvoltage or so at all, but to break the current feed to the arresters, so just extinguish the arcs there and restore them back into non conductive state.

So the lineman was right about where the lighting current flows, about the automatic shutting down the line temporarily, but wrong about the purpose of that interruption...

Interesting. There goes my dream of potentially having a motion detector high bay.

You can do that with a HID light, if you use two capacitors and are willing to accept a dual level or step level dimming arrangement allowing the HID to dim while not in use and brighten when motion is detected, and dim again when the motion stops.. Normally this can be done with the original ballast, you just need two capacitors and a relay to either add or remove the second capacitor, depending on if you set up your capacitor in a series or parallel configuration. It's also a good idea to allow a HID's to fully warm up for like 30 mins before dimming them.

About the only draw back is the color of stepped dimming hids can suffer when dimmed but at least you can see what your doing, but you can reduce the input watts by about 40% which reduces the light output by about 60% and the lights warm up fairly quickly, and if you don't dim more then 50% (input power) you only lose like 10% of the lamps operating hours at the max but the power saving more then recover this, but i'll warn you,if you go  more then 50% input power and it quickly goes up to 90%. but on the plus side this works on MV,HPS, and MH.

Or you could always use a hot a re-strike igniter if you have to turn the lamp off. But make sure the lamp, socket and wiring are rated for a hot re-strike igniter, some high end instant units can output like 40KV but they will instantly restart a hot or cold tube on the next AC line cycle, even those hard to start ones, or a small cheaper one like the Advance one which will do it in under 2 seconds it still outputs like 5KV, they are almost like automotive HID light ballasts in operation, you can flash HID lights in a car fairly fast and you can do the same with larger HID if you use the right equipment.