2003 Ford Mustang Wipers and Turn Signal

Hello mach1mustang777

Welcome to 2carpros

You are dealing with a short to ground, before the grounding switch. (Because there is no blown fuse) or a short to power between connectors. And corrosion in connectors could be the problem.
Before hunting for short, lets check the basics.
In the battery junction box, there are 2 relays:
Wiper high/low relay, wiper park/run relay. check those two.(one of them may sticks)
If the relays are good, on the wiper/low relay side, there are 4 connectors before the wiper motor.( check for corrosion in those)
On the wiper par/run relay side there are 3 connectors before the wiper motor. (Check those) look also for burn wiring insulator on that side.
For the park /turn lamp left front, check the ground as indicated. Check for open between the switch and the bulb.

here is the wiper diagram and its related connectors.

here is front left turn signal diagram .
Check your email for those 2 diagrams