I know it shouldn't happen but in case it happens for whatever reason, what is correct procedure to save the day. I mean the case that the aircraft is turning but it gets to the wrong side by, let's say, one, maybe two deg, so the pilot or autopilot has to make the correction and "fly back" to LOC.
I guess the ATC won't be happy, due to separation, protected areas of parallel runway or so.
But how to solve that? Can the aircraft fly back to LOC on its own, still asume it is within LOC deviation scale and we can see the diamond? Should they inform ATC that they will be on the wrong side for a while? Do they have to be vectored back to ILS again? I ask specificaly for this because I was told so but it seems to be quite ridiculous to issue a new vectoring for few seconds because before it will happen the aircraft will be already turning to LOC and it will be useless.