It could be a broken wire, it could be bad contacts. The net result is the same - the circuit is open, and not passing electricity.

At the risk of restating what has been said previously, the design is NECESSARY when the bigger/brighter filament in the bulbs at the rear of the car perform TWO functions - turn signal and brake. Imagine following behind yourself as you slow for a right turn: You apply the brakes at the same time that you are signaling for the turn. The left side brake light stays on solid, and the right side BLINKS. This is accomplished by routing the brake light circuit through the turn signal switch. Every time you signal one way or the other, the brake light circuit on that side OPENS (regardless if you are stepping on the brakes or not), and power from the flasher is applied instead. The signaling that happens day after day, year after year wears the contacts out so that they no longer make a circuit even when you are not signaling. It's just a fact of life of this particular design.

You can avoid it by never signaling again, or driving a car with separate [amber] turn signals at the rear.