Would like to understand this about GL_LIGHT

Code:

 // GL lights initialization:
glLightfv(GL_LIGHT2, GL_AMBIENT, LightAmbient);
 
glLightfv(GL_LIGHT1, GL_DIFFUSE, LightDiffuse);
glLightfv(GL_LIGHT1, GL_POSITION,LightPosition);
glLightf(GL_LIGHT1, GL_SPOT_CUTOFF,90.0f);
glLightfv(GL_LIGHT1, GL_SPOT_DIRECTION, LightSpotDirection);
glLightf(GL_LIGHT1,GL_SPOT_EXPONENT,0.4f);
glEnable(GL_LIGHT1); 
glEnable(GL_LIGHT2);

Notice I used GL_LIGHT2 only for the ambient light.
Right now it is working the way I want, but if I simply change it to GL_LIGHT1, the ambient light gets way, way darker.

Any ideas why this happens?

because of this line

Code:

glLightf(GL_LIGHT1,GL_SPOT_EXPONENT,0.4f);

I am pretty sure at least.

Uhm, I tried testing with all lights set to 1, and the darkness only occurs when I enable GL_SPOT_CUTOFF. Then I tried changing the spot exponent value, but nothing seemed to change, even if it is set to 0.01f.
But anyway, shouldn´t the ambient light be completely independent from any diffuse lights? At least I was sure so