How can i restart a timer?

A few things are to be noted about your code:

First up is that you should not have a while loop with the condition != 0f This is not safe imo when dealing with floats. Please go for >= 0f instead.

Secondly why WaitForSeconds(PadTime / PadTime); This is WaitForSeconds(1f); right?

But most importantly:

  StopCoroutine(PadTimer());

This does not do what you think it does. If you want this coroutine to end then just exit the function. This can be forced with yield break; as a similarity to return in a normal function but just letting the function end like any other as well is enough.

If you want to use StopCoroutine correctly you have to do it like this:

  routineReference = PadTimer()
  StartCoroutine(routineReference);
  ...
  // do something and somewhere else cancel it:
  ...
  StopCoroutine(routineReference);

Most importantly your issue is Probably that you do not reset PadTimer once it has reached zero. This is probably the issue why you cannot restart it since it always directly exits your Routine.

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 
 public class TimedPressurePad : MonoBehaviour
 {
     public float padTime = 5f;
     public Material pressed;
     public Material unpressed;
     public Renderer padRenderer;
 
     // Fill the inspector with the one, two, three, four and five pads
     // First element = [0..1[ second
     // Second element = [1..2[ second
     // ...
     // Fifth element = [4..5[ second
     // ... 
     public Material[] timerMaterials;
 
     private void OnTriggerEnter(Collider other)
     {
         StopAllCoroutines();
         StartCoroutine(ChangePadMaterial());
     }
 
     IEnumerator ChangePadMaterial()
     {
         int index = Mathf.Min(Mathf.FloorToInt(padTime - 0.01f), timerMaterials.Length - 1);
 
         if(index >= 0 && !Mathf.Approximately(index, padTime))
         {
             padRenderer.material = timerMaterials[index];
             yield return new WaitForSeconds(padTime - index);
             index--;
         }
 
         WaitForSeconds wait = new WaitForSeconds(1);
         for(; index >= 0 ; index -= 1)
         {
             padRenderer.material = timerMaterials[index];
             yield return wait;
         }
         
         padRenderer.material = unpressed;
     }
 }