One way to prevent the dimming is to block the light sensors in the rear view mirror. I sometimes use an elastic wrist sweatband to do this. Slide it over the left side of the mirror so it blocks both the sensor looking forward (on the back of the mirror housing), and directly on the other side of that on the mirrored part is a sensor looking back (it's not visible except at some angles). A wide rubber band should work as well if placed exactly right. A sweatband covers part of the mirror but it's still quite useable.
The sensors seem to work in tandem such that when the light seen by the forward looking sensor is dimmer than the light seen by the backwards looking sensor, the mirrors dim. They dim pretty quickly, but undim much slower. You can use your hand to block the mirrored side temporarily, but it takes a long time to undim. In a pinch I've pushed a glove over the entire left side of the mirror.
It's not pretty, but it works.