Parking lights and turn signals not working

Your description is confusing. At one point you say lights work, then you say they don't work. Which lights do not work? Front, rear, one side, etc.

Since I have bought the car the parking lights have not worked when the headlight are on. The turn signals and 4 way flashers did work. I replaced a fuse in the fuse box and after that the parking lights did work for several days after that. However now neither the parking lights or the turn signals work on this car.

The lights that have given me the problem are the rear parking lights.

If the front running lights work, that leaves out the headlight switch as the problem.

Lets start with the tail lights. When we solve that we might solve the signal light problem too. The only thing all the tail lights have in common is the ground wire. That should also cause the brake lights and backup lights to not work, however, those can be misleading because they can find an alternate path to ground through the front running lights ONLY when they are not turned on. That means the brake lights will be dim until a helper turns the headlights on, then the brake lights will go out.

If the brake lights and backup lights work normally regardless if the headlights are on or off, that proves the rear ground wire is okay. (It's on the left rear quarter panel). There are three different circuits for the rear tail lights. It's unlikely all three would develop a problem at the same time. Check to see if the license plate lamps work. If at least one of them does, that will narrow down the list of possibilities. If both do not work, check if they're burned out. Those two get overlooked a lot. If the bulbs are good but they don't turn on, we'll have to look in the parts of the circuit they have in common with the tail lights.