Can your pupils still dilate even when you have bright light shining on them and extremely near them?
Yes, if you are blind or temporarily blind. This happened to me after an eye surgery on my right eye. The right eye was patched but I could not see ANYTHING from my left eye, which had not been touched. The doctor was shining light into my left eye, (so the told me later), and it was completely dilated. Turns out the anesthetic used in my right eye traveled up the optic nerve where it joins with the left eye and temporarily blinded me. Thankfully, the vision returned fully in about an hour.
That is pretty much what happens during many eye exams. Drops are put in the eyes to dilate them. The doctor then looks in the eyes with bright lights.