how to open the tailgate when the handle is broken?

Use a Phillips head screwdriver, but you can only do this about 5 times, as you bend the inners. Put it through the hole under the broken pull handle, the hole is to the right behind the handle, At an upward angle, fell for the window (should be all the way up) and then just below, you can fell the latch, pull upward wedging/pivoting against the rear body license plate trim (the big fiberglass piece that holds the license plate) It may take a few time sto get it right.

The plastic handle broke on my 2002 Sequoia tailgate. Here is a way to open the gate: 1 - Run the window all the way down, and then run it up about 1 inch. 2 - Wedge the window forward by placing a wedge or shim behind the window and gently force it forward until you have about 1/4 to 1/2 inch space between the window and the window gasket. Place the wedge about in the middle of the window. 3 - With a good flashlight, look down into the window slot just to the left of the middle of the gate, and you will see a plastic cable sheath leading to the right. and a bit of cable and a ball on the end of the cable. There may be a piece of the broken latch mechanism attached to it. 4 - You will need a 16" or so piece of wire coat hanger or some similar bendable but strong wire. Put a "U" shaped bend in the end with about 1/8" inside measure. Now bend the "U" so it is at about right angles to the length of wire. 5 - You may have to adjust the shape of the wire leading to the "U" so that it can be positioned around the ball at the end of the cable. It may be advantageous to feed the wire from the right side of the wedge as you will probably need to pull up and to the right on the ball and cable. There is an electrical cable that blocks your view to the right, but the cable mechanism should be visible just to the left of center above the license plate (Inside the gate) 6 - Pull gently up and to the right. It may help to push the gate closed initially to release the strain on the latch before pulling on the cable and a friend might be helpful here. You should hear a click as the latch releases and the gate can be pulled open.

Here is a youtube video that discussed. I had success using a 90 degree angled needle nosed pliers. http://www.youtube.com/watch?v=30mb2rNf46I