Im not 100% sure but it sounds like a switch issue.
Nope. The other side works, so we know the switch is working. It also works when using the turn signal, so kaleoaga is correct that it's not a ground issue. Have you checked the bulb to see if the parking light filament is bad? If it's good, then you know the issue is wiring between the switch and the bulb.
What I do see is a rat's nest of wires with a chintzy crimp connector and a bread-tie. I don't mind crimp connectors, but they need to be the good heat-shrink ones. Crimp, tug test, and then shrink. Never use wire ties to hold wiring. Instead, trim that excess wire length.
Get out that test light and start looking for where the power ends.