I think there are two sensors - 1 on the mirror side, on top middle (the one to cover up) and another on the front of the mirror, on the passenger side. I am guessing that the computer takes the difference in brightness between the two sensors - I tried putting a small flashlight to the front sensor, and that also disabled the dimming. Obviously not very practical - much easier to block the rear sensor.
One easy way is to take a post-it, make it black with a pen, and then use a paper hole puncher to make a round dot from the sticky side of the post-it. It's just the right size to cover the sensor. Cheap, easy, and easy to remove if you don't like it.