Above the pedal should be a button, with 2 wires coming out of it. When your pedal is up, the button will be pressed all the way down, as you press the pedal, be button will release. At some point this button turns on your tail lights.
I know the one on my truck is adjustable (because I've had to adjust it). In this case, you remove the wires from the back and spin it to the proper location. You will want the sensor further from the pedal to have the lights come on earlier. Use a mirror or have a friend watch to ensure you have the proper adjustment and they do not stay on when you are not touching the pedal.
In the case the switch is not adjustable, you have 3 options. Replace the switch with a new one to see if it is any better. Modify the switch. This can be done in 2 ways - shave down the top of the button head so the plunger is further out, or open it up and clean/move/change the contacts. The third option is to modify the pedal or mounting. You may be able to bend the tab that hit the button's plunger, or the bracket the switch sits in.