FZS1000s don't have ECUs, they have an igniter unit/box in the tail hump. As far as I'm aware there's no connection between the cooling fan cutting in/out and the igniter box, the bikes system isn't closed loop, it has a now old fashioned CDI type system, I won't go into to details.
From the sounds of what your describing, you've got water ingress either in the ignitor box, starter relay, staring circuit cut off relay. it's also possible there's an issue with the rectifier/regulator. Remove all the plugs to all of them, check for corrosion, clean and try if that doesn't work it's highly likely there's water in the ignitor box. This will slowly heat up causing a vapour that will short out the unit and stop the bike, it condenses on cooling down the bike restarts, this will happen with alarming time accuracy 20/30mins or so.
It happens to proper ECU's, they have to be opened dried or replaced.
Check all the connections and test all the components first. If they're all ok, swap the ignitor box, you can try and borrow one from a known running bike first, to replace they're approx £80 second hand.