Exterior lighting issue

"right turn indicator in the dash stays on"
That clearly shows a fault with ground

X2. I'd pull all sockets, front and rear, clean or replace, replace pigtails if they look bad, and clean or replace the bulbs.

Don't be afraid (if you can solder) to attach ground pigtails to the socket shells so that you can ground them well. For the tail lights, you can run an additional wire from each one over to the trunk latch bolts