Sorry guys, I was (and am) busy with other things, but I have read everything you posted.
LEDs will be on the wings of the RC plane - so I can't guarantee they will both see each other (fuselage in between), construction is not exactly rigid, and they will be mounted using velcro. It all makes me doubt IR and photocell solutions will work, as the line of sight can be obscured and I can't guarantee directionality of the LED and photocell (and I assume it is necessary). I have nice lights on other model, controlled with Arduino and whatnot, but this time I need an easily removable solution that can be used on any model.
I have a chest strap-based heart rate monitor that apparently communicates with the handlebar mounted display using a radio. I believe all the chest sensor does is it is sending a pulse for each heart beat, this is more or less kind of a solution I was thinking about (and would be satisfactory). (Actually if you can suggest what frequency it can use I could try to check if that's how it works using RTL-SDR scanner).
Yes, there is a potential problem with LEDs getting out of synch if the pulse is used just for toggling the state. At the same time if I am able to just make them start the pulse at the same time and use 555 to keep the pulse length mostly identical on both wings it should be enough.
They will never work for longer than about 30 minutes
I will look into remotes.