2008 sable premier brake lights will come on after the car is turned off even if they are off, they sometimes just come back on. Sometimes you have to hit the brakes a number of times to get the brake lights off too.

SOURCE: My brake lights won't turn off. even when vehicle

Sounds like either your brake pedal switch has somehow gotten misaligned or gone bad. Look at the top of the brake pedal and find the switch. When you push in on the brake pedal the upper part of the pedal should contact a movable button on the switch and move it either in or out (depending on which side of the pedal the switch is on). If you can see the switch contact being moved, and the lights still stay on, it sounds like the switch itself is bad.

SOURCE: 2002 Mercury Sable-shakes with acceleration

You describe this as an acceleration problem however, if the car does throw a check engine light it should be recorded in system memory so it can be pulled by scanning with and OBDII scanner. It sounds as if the car is being starved for fuel on acceleration. Check the fuel lines for kinks as well as check the fuel pressure. The problem could be a faulty fuel pump that has yet to completely die.

SOURCE: Rear brake lights remain on.

just simply unplug connector from brake switch located at base of brake pedal, if lights go out switch is bad, if lights do not go out you have a short to power on brake lamp circut before turn signal switch