Ok, this is getting more and more common. Not sure on the one front one rear thing but for now, may just be more resistance in those units:-
The reason is to do with the bike's wiring. On a bike with normal filament bulbs in the indicators there is a power draw of obviously 42 watts (plus a bit for losses) this needs power ie amps to make it happen. Bit of ohms law and we know your using 3.5 amps or thereabouts.
The 3.5 amps is the key to the problem, LED lamps use milliamps to power them and this is the cause. The little bulb in the dash lights up when you turn left or right. It is actually connected to both left and right circuits on the bike but due to the vagaries of electricity there will not be enough power after the dash lamp (it only draws around 1/2 amp or less)to power the othr indicators so the electric just runs to earth through the filaments but doesent actually light them up, (we need 3.5A for that remember)
With the LED lamps its different, they only need milliamps to make them work so when the dash lamp earths through the opposite side to that which you want, the 1/2 amp or so thats running to earth will happily power them up. Giving a 4 way flasher effect.
You have a couple of options, fitting diodes like the rectifiers on early trailee's like mine. One side of the dash lamp would have BOTH feeds to it via the diodes with the other to earth. (My personall favorite soloution). You could fit resistors to each side of the dash lamp. Not sure how big you need them as you may affect how bright the little dash lamp is. Or simply fit another dash lamp so you have one for the left and one for the right.
The easiest method for now is to take the bulb out the dash. As this simple action splits the connection between the circuits. Then the problem can wait till MOT time if need be.