No, not the relay, that's before the circuit branches to L/R at the switch - the diode array at the indicator lamp.
Just my best semi-educated guess:
I'm thinking that the voltage (think of volts as electrical 'pressure' & the wiring as plumbing) is 'leaking' a bit past 2 of the 4 diodes (one-way 'valves' ) shown in the 2nd diagram fullthrottle posted. They are there to isolate the R & L branches of the circuit from being bridged by the single dash indicator light (one pair allows current to flow thru the indicator when L is switched on while the other pair blocks current to the R, and vice-versa when R is switched on).
But I think the diodes aren't blocking the voltage completely, so when one side flashes at full 13~14V, the other side also energizes to say 3 or 4V - not enough to make the filament of a regular bulb glow, but enough to dimly light the replacement LEDs. I think the reason the fronts aren't doing it is because they have series resistors built into them which are of a high enough resistance to keep the LED's from reaching their 'threshhold voltage' (the point at which they emit light). So I'm thinking he simply needs to add a resistor (or replace existing ones with higher value) to limit the voltage the LED's are 'seeing' & keep them below that threshhold. But I could be completely wrong & just wasting time trying to remember what little bit of electronics I learned years ago - hey, it beats doing a crossword puzzle though!
