What could be the reason for the brake lights and turn signals to stop working on a 1989 Pontiac Acclaim?

Is it a Plymouth Acclaim? Never heard of a "Pontiac Acclaim" The first place to start looking is in the fuse box. most likely located on the driver side. either under the dash, Or behind the "kick panel" (where your left foot would kick against) to the left of the pedals. After locating the fuse box (fuse panel) find the fuse labeled "brake light" or "tail light" or "turn signal" Pull out one of these fuses (one at a time) inspect the fuses condition. If its burned "blown", replace it with a new one of the same amp value as the one that you have removed. If after replacing the burned fuse/fuses the new fuse burns out shortly or immediately after installation, It will indicate that you have an electrical short and the vehical will need to be diagnosed by an auto electric shop, Or by a Mechanic with electrical experience.