Gameobject script enable weird behavior

I have a rather simple gameobject with three scripts, amongst which a simple one with an OnMousedown() function, that performs correctly and prints to console.

I have the need to disable the simple script after three clicks, and I thought well this seems pretty straightforward so I came up with this:

 int maxclicksallowed = 3;
 int clicks = 0;

 void Update() {
   //do the update stuff
 }

 void OnMouseDown() {
 
   if (clicks > maxclicksallowed) {
     //this actually works: the script gets disabled in the inspector
     gameObject.GetComponent<thisscriptclass>().enabled = false;
     print("how dare you click so much, I'm deactivating this script");
 
   }
   else {
     //do the stuff i normally do
     //...
     clicks++;
   }
 }

Curious and unexpected thing is, despite the script being disabled in the inspector (the checkbox gets unflagged), mouse clicks on the object will still print the message, so WTF?

I don't like the idea of destroying the component script since it holds runtime state variables of the object that I'd need to save in some convolute way, and I don't like the idea of using a boolean condition, since the object will keep calling its update function "for nothing" (since it'll skip thanks to the false boolean condition mentioned).

So I'm ultimately wondering: what's the best way to 'disable' a script and prevent it's execution and Update calls until reactivation?

Thanks