First, a cleaner version of a basic counter:

great work with the timer. it's more of a brain bender than one would imagine, i think.  what about this?

some notes:

1) I've moved your timer out of draw into it's own function.  May not be a necessity, but I think separating things out into methods/functions helps with tracking down bugs.  As you advance in Processing, you'll need them anyway.

2) I'm using mousePressed() to pick up on click event.  Then, I make sure that the mouse is within the bounds of the box.  If it is, it changes boolean start (declared above setup) from true to false and back again.

3) Finally, I put a test inside the timer() function to see if start was true or not.'

4) Also added background(155) in draw so that the timer text wouldn't draw on top of itself.

1. boolean start = false;
   
   void setup(){
       size (340,340);
2.     background(155);
       rectMode(CENTER);
   }
   
   void draw(){
       background(155);
       rect(width/2,height/2,50,50);
       timer();      
   }
   
   
   void mousePressed(){
       //if the mouse is in the box
       if( (mouseX <= width/2 + 25 && mouseX >= width/2 - 25) &&
           (mouseY <= height/2 + 25 && mouseY >= height/2 - 25) ) {
            start = !start;  //turns start on and off
            fill(255);
         }
   }
   
   
   void timer(){
     if(start){
         int times = millis();
         int timem = millis();
         int timeh = millis();
         textSize(32);
         fill(0,0,0);
         text((times / 1000), 10 , 195);
     }
   }
   

also, what tfguy44 said.

And a counter that does minutes and hours too (untested):

isOver() is a function that determines if the mouse pointer is over the rectangle.
If you're getting an expected token, you might be missing a curly bracket.

If you edit lines 165 to 167 to check if the mouse is over your button, it works just fine:

You can make it do whatever you like!

But that sort of a timer is a little trickier. You'll need two buttons, one to pause/play and one to reset, a boolean to track if the timer is going, and an additional int to keep track of the additional elapsed time.