The instruments are all part of what Yamaha refer to as the "Multi-function meter". It is this that determines the neutral light and so on. The ECU is a separate black box that sits under your saddle, that is most unlikely to be relevant to your issues.
Again, I also think it unlikely that the multi-function meter is the cause of your problem unless it was physically damaged in your incident. Much more likely to be something external to it, particularly the multifunction relay, which is in a vulnerable place and has much of the relevant wiring going through it.
The backup fuse does supply the odometer, so your miles won't be recorded, generally not a good thing. I don't know how much else it supplies, does the speedometer work? If not, I suspect the bike would be considered illegal (certainly the case in the UK), and it is very difficult to know how fast you are going on an FJR, so unwise to ride if it isn't working. Does it supply the fuel gauge? That could be embarrassing if that doesn't work - at this stage the trip won't work either so you will have no idea how far you've been on this tank of petrol. (Reminds me of my old Tiger Cub days, rock the bike, judge how much fuel you have by listening to it sloshing in the tank!)
If you do change the multi-function meter (which I suspect is what your shop was referring to, not the ECU), do make sure the odometer reading of the old unit and the replacement unit are recorded.
