What is wrong with an 87 Cougar if the hazards work fine there is no blown fuses all bulbs are good but the blinkers do not work and if brakes are applied when the switch is on the taillights dim?

I haven't run into that particular problem in a Cougar, but the systems in most cars are similar enough to offer a few clues: First, an education, that's free. If the vehicle uses the same lights for brakes, turn signals and hazards; and not separate turn signals, then all these functions have to be routed through the turn signal switch, in the steering column. This is usually a pain to change, but they often develop problems... Try to imagine how much they are used. In your case, I would first make sure all the lights are grounded well, but this is just proceedural, because the hazards work. As much as you're not going to enjoy changing it, the turn signal switch in the steering column is most likely the culprit. Sorry, but it does give you an opportunity to clean out the column... :)