Which neurological disorder causes a person to either stop talking or talk too much?

If the loss of speech is rapid, can be a stroke.

Loss of speech can be observed in patients with multiple sclerosis, but in this case, there are other, more significant symptoms.

If loss of speech is recurrent, it can be symptom of disorganized or catatonic schyzophrenia. Also with other symptoms as disorganised thinking or sudden freezing of body.

Also loss of speech can be observed after sudden traumatic experience.

Brain trauma, epilepsy, and brain hemmorage or brain tumour, can cause brain damage causing loss of speech.

Also patient, may not want to speak, it is possible.

Possible is damage to vocal chords.

In case of talking too much, there can be few explanations.

Tourette syndrome is one of them. Characterized by tics and sudden vocal expressions.

Also abuse of drugs as methamphetamine, can cause thought flow.

People with ADHD can cause effusive concentration to debate, and thus, patients cannot easily stop their monologue.

Also, in manic phase of bipolar disorder, patients are unstoppable in their thought flow.

Asperger's patients are also known to talking too much.

Persons with Narcissistic personality disorder are used to talking too much, and be always centre of attention.

There are many, many explanations, but in every case, you have to consider other symptoms.

But, in way as you formalised your question, you are asking of sudden changes of mutism and rapid talk. I bet on rapid cycling bipolar disease, with sudden changes in depression and manic phase. Or disorganized schizophrenia with disorganized thought flow and rapid moments of sudden mutism. In every cases, it is not normal, and person should search for help.

 Reference: Michal Stefancík