Sometimes the connector for the temp on the rear cilinder also EFIes
The exact simptoms as you described, efies at the start, then usualy stops, but it has its days when it efies all the time.
It does efect the motor running (but not enought to notice it), because it has no info for the temp it sends the most rich mixture to the engine, same as if the engine would be cold.
Fix is simple, just nudge some wires a bit, on my bike it helps if you nudge the wires on the left side above the radiator, if you sit on the bike and put your hand in the hole in the fairing, on top you feel some wiring, if you nudge it the ******* EFI goes away. I fixed it by sorting the cables a bit, no EFI since then
(and life is good again(if you dont count the front light not working
))