Unfortunately, the word amplitude can mean different things. Mathematically, the amplitude of a vector is just its length, so by definition it never goes negative because negativity is contained in the directional part of the vector and not in the length. In physics, "amplitude". Also in mathematics, amplitude can refer to the magnitude of a complex number, which is also always positive. Finally in physics, "amplitude" can mean the part of the wave's functional form left after the waving part has been isolated away. Used in this sense, the amplitude can be negative. The problem is that EM waves are complex-valued, waving, vector fields. This means that the word "amplitude" is present in all three forms in EM waves, and we must be more specific in relaying which one is meant.
In my previous comment, I meant the amplitude in the sense of what is left when the waving part is put to the side. So if the wave is E = E0 cos(kx - ωt) then the light intensity is proportional to |E0|^2.