You're on the right track, but you have a major problem in your code.  Let's say second() = 30.  Then when this code runs:

Code:

while(s < 59){
  // Whatever here
} 
 

You will be stuck in an infinite loop!  Since 30 is always less than 59, the program will never exit this loop.  Processing only updates the window at the end of draw() so the result will be a frozen, blank applet.

Since the draw() functions loops on its own, you don't need a while loop at all.  Instead, everytime through draw, check and see if the seconds have changed (using a "global" variable to keep track of what the seconds were the previous time through draw) and then draw your ellipse:

i.e.:

Code:

int s;
 
void draw() {
  int newS = second();
  if (newS != s) {
    // do something
  }
  s = newS;
}