Sounds like your light switch or steering column turn signal mech is buggered up, somewhere you have a wire/switch crossed or shorted. If the previous owner did a eng swap.... very possible they played with the wires out of the column.
You need to determine if it's the turn signals or the parking lights getting the cross feed, you should have a dual filament bulb and it would help if you knew what side to chase….
Remove the lens covers and see which filament in each bulb is doing what, not if the light lights…..
Do the haz flashers work both front and rear?
Do the turn signals work both front and rear?
Do the parking lights work both front and rear?
Do the brake lights work in the rear?
The front parking lights are fed from the headlight switch on one filament of the bulb.
The front and rear turn signals are fed from the steering column turn sig mech, on the other filament.
The rear parking lights are fed from the headlight switch
The rear turn/brake lights are fed from the brake light switch thru the turn signal mech..... that once again is located in the steering column.
From your symptoms it sounds as tho’ the brake light feed is bleeding over into the front turn sig lights….. not the parking lights,….The only common area is the turn sig mech located in the steering column. The turn sig mech interupts the brake light feed to allow the rear turn sig to work when you step on the brake etc.... Now this is based off-of.......Do I remember correctly......lol