So the way that alzheimers disease works is not by signal delay but in wrong interpretations. Its like translating French-English but the input is Spanish. There are words that are similar enough to get the point but sentence is still nonsensical.

There is still an appropriate pain response but theres also delusion/hallucination.

Someone with peripheral neuropathy, such as from diabetes or ALS, can have delayed or no response (sometimes phantom signals).