Right front turn signal blinking fast

You gave a perfect description of what happens when two or more bulbs share a common ground that has a break in it. A signal bulb will act differently depending on whether the bulb in the other circuit is turned on or off.

This diagram shows the ground wire for the right front turn signal bulb, (blue arrow), shares ground # G104 with the right low and high-beam head lights, (purple arrow). What they don't show is whether both wires are crimped into a single terminal that's bolted to the body sheet metal, or if the two wires are spliced together, and then a single wire is in that terminal. If both wires are in the terminal and that terminal is loose of corroded, most likely the right head light would be very dim or not work at all.

The best way to approach this is to measure the voltage on the black / pink ground wire at the signal bulb's socket. To be valid, that has to be done with the bulb in the socket and the right front circuit powered up. This should work better if you use the parking lights instead of the signals. The signal circuit will flash on and off too fast for the voltmeter to respond.

If you need a voltmeter, you can find an inexpensive one at Harbor Freight Tools for around $7.00. Walmart, any hardware store, and all auto parts stores have them too. This article:

https://www.2carpros.com/articles/how-to-use-a-voltmeter

shows how to use it. They're using one with the "auto-ranging" feature that inexpensive meters don't have. I can help you set yours up if you need it

That black / pink wire should have 0.00 volts on it all the time. In real life you may find a few hundredths of a volt. That can be ignored. Treat it as 0 volts. With this symptom, expect to find a substantial voltage on this wire, perhaps around 2 to 11 volts. That would be proof there's a break in that wire between where you have that voltmeter probe and where that wire bolts to the body. If you should find 0 volts, that would indicate the break is between the location of the voltmeter probe and the terminal on the bulb.

Let me know what you find.