It looks like you've tried to record when the last motion occurred by setting the secounds variable when you detect some motion but you've not used this variable anywhere else so it's not going to have an effect on the timer.  The code below resets the timer when a pixel exceeds your motion threshold by recording the time of the last motion to a global variable called lastMov and then subtracting it from where you work out the current time at the end (lines 12, 63 and 74).

Also, there's no need to use nested for loops for x and y and then converting to an array location.  The pixel array for the previous and current frames are the same size so you can just loop through the raw array and the locations will match up.  I've not made this change.

Finally, please properly format your code before you post it - use cmd-t (on a Mac) or ctrl-t (on Windows/Linux) to clean up the indentation and remove excess blank lines.

1. //  motion detection with stop watch that resets when movement is detected. 
2. import processing.video.*;
3. 
   
4. // Variable for capture device
5. Capture video;
6. 
   
7. // Previous Frame
8. PImage prevFrame;
9. 
   
10. // How different must a pixel be to be a "motion" pixel
11. float threshold = 80;
12. float lastMov;
13. 
    
14. float TextFont;
15. 
    
16. void setup() {
17.   size(1300, 800);
18.   video = new Capture(this, width, height, 30);
19. 
    
20.   // Create an empty image the same size as the video
21.   prevFrame = createImage(video.width, video.height, RGB);
22. 
    
23.   //PFont font= loadFont("Verdana-12.vlw");
24.   //textFont(font);
25.   lastMov = 0;
26. }
27. 
    
28. void draw() {
29.   // Capture video
30.   if (video.available()) {
31.     // Save previous frame for motion detection!!
32.     prevFrame.copy(video, 0, 0, video.width, video.height, 0, 0, video.width, video.height); // Before we read the new frame, we always save the previous frame for comparison!
33.     prevFrame.updatePixels();
34.     video.read();
35.   }
36. 
    
37.   loadPixels();
38.   video.loadPixels();
39.   prevFrame.loadPixels();
40. 
    
41.   // Begin loop to walk through every pixel
42.   for (int x = 0; x < video.width; x ++ ) {
43.     for (int y = 0; y < video.height; y ++ ) {
44. 
    
45.       int loc = x + y*video.width;            // Step 1, what is the 1D pixel location
46.       color current = video.pixels[loc];      // Step 2, what is the current color
47.       color previous = prevFrame.pixels[loc]; // Step 3, what is the previous color
48. 
    
49.       // Step 4, compare colors (previous vs. current)
50.       float r1 = red(current); 
51.       float g1 = green(current); 
52.       float b1 = blue(current);
53.       float r2 = red(previous); 
54.       float g2 = green(previous); 
55.       float b2 = blue(previous);
56.       float diff = dist(r1, g1, b1, r2, g2, b2);
57. 
    
58.       // Step 5, How different are the colors?
59.       // If the color at that pixel has changed, then there is motion at that pixel.
60.       if (diff > threshold) { 
61.         // If motion, display black
62.         pixels[loc] = color(0);
63.         lastMov = millis() / 1000;
64.       } 
65.       else {
66.         // If not, display white
67.         pixels[loc] = color(255);
68.       }
69.     }
70.   }
71.   updatePixels();
72. 
    
73.   int seconds = millis() / 1000;
74.   seconds -= int(lastMov);
75.   int minutes = seconds / 60;
76.   fill(0, 0, 0);
77.   seconds -= minutes * 60;
78.   text((minutes) + ":" + (seconds), width/2, height/2);
79. }