One way to look at it is that light is a electromagnetic wave ie a form of energy.. it doesn’t consist of charged particles and thus it won’t be deflected by electric and magnetic fields.
Now you might think that it is possible that the electric and magnetic field are in such a way that the resultant (applied, em wave’s) magnetic and electric field are no longer perpendicular to each other and thus the EM wave kind of gets destroyed..
This is incorrect because: an EM wave is a time varying as well as position varying electric field wave and magnetic field wave coupled.. if we observe at a certain position ie removing the position dependency, now only the factor of time comes into play.. so even if the resultant electric and magnetic field are not perpendicular, the time varying factor of both will be the same as earlier.. and for EM waves we will consider only the time varying factor of of both fields which will be perpendicular as earlier.. thus the EM waves is not deflected..
Hence, it might be true that EM waves get deflected by a time varying electric field and/or time varying magnetic field.. ie a EM wave might be deflected by another EM wave….
The second reason is my thought only, I am not sure if it is correct
This was my first answer on this platform!
Thank you