Why is the second ball not illuminated yet, but it is on the next bounce?
Also, why doesn't the light source have any light bouncing off of it like the rest of the ceiling?
@leonxu1 I believe it is but now on the face towards us.
I'm not sure about your second question but it seems like we're not considering effects of bounces off the light source since it's the source and we can think of it as having maximum brightness
For the second ball, since it is made of a material that both reflects and refracts, in order for the side close to us to be illuminated, light must bounce 3 times before we are able to see it.
For your second question, for light sources we only consider the emitted light term.