They switch off in day light...
Is that light on permanently or a free running flashing?
Does it ever come back on?
The sync control doesn't have to "travel" in the same direction as the "moving light" travels.
Lamp sequence: ... 6 ¦ 1 2 3 4 5 6 ¦ 1 ...
The 1-6 block:
Lamp 1 on turns off lamp 6 of the previous block after 200 ms Lamp 2 on turns off lamp 1 after 200 ms Lamp 3 on turns off lamp 2 after 200 ms Lamp 4 on turns off lamp 3 after 200 ms Lamp 5 on turns off lamp 4 after 200 ms Lamp 6 on turns off lamp 5 after 200 ms Lamp 1 of the next block on turns off lamp 6 after 200 ms
Lamps come on 1.2 seconds after being switched off.
I think that will work and self sync. Timing an accurate 1.2 seconds from a known point in real time is a POP.