Left turn signal blinking fast

The simple, reliable, three dollar signal flasher has been replaced with an unnecessarily-complicated body computer. There are two separate output circuits, one for the left rear and one for the left front, so one working bulb can no longer be used as a clue.

Go to the light blue/white wire in the left front bulb's socket, and measure the voltage there. You should see it pulse on and off when the signals are turned on. If you do find voltage there, the ground wire has a break in it. If no voltage appears on that wire, find it at the body computer or at the under-hood fuse box. The wire originates at terminal four at the body computer, behind the center of the dash, then goes through the fuse box, in terminal ten, and out on terminal three. All are light blue/white wires. If you find the pulsing twelve volts there, there is a break in that wire. If there is no voltage on that wire, suspect the body computer.

There is twelve volts where, at the body computer, the fuse box or the bulb's socket?

Dandy. If that voltage is pulsing on and off, that just leaves the ground wire. You can verify that by measuring the resistance with an ohm meter. Also, if you can get to the terminals with the bulb in place, you'll find 12 volts on both terminals. You should not have 12 volts on the ground terminal.

Think of a garden hose. Voltage is electrical pressure just like the water is under pressure. You have 12 pounds of pressure at the faucet and 0 pounds after the water leaves the nozzle. As a result, water flows through the hose from the higher pressure to the lower pressure.

You need 12 volts of pressure on one terminal of the bulb, and 0 volts on the other terminal. That difference in electrical pressures is what makes current flow, and that's what makes the bulb glow.

If you turn the nozzle off, water flow through the hose stops, and you will measure 12 pounds of pressure at the faucet, AND at the nozzle. The difference in the two pressures is 0 pounds, so there's nothing making the water flow through the hose.

Same with the bulb. A cut or corroded ground wire is the same as turning the nozzle off. You'll see the 12 volts on the feed terminal, (like normal), AND on the ground terminal, and all the way along the ground wire up to the point of the break. The stipulation is the bulb has to be in the circuit.

Similarly, while this sounds silly, the only way to see 12 pounds at the turned-off nozzle is the hose has to be there.

This is much easier to explain when you're in front of a chalk board, but all you have to do is take the readings I give you then I'll analyze them. I don't know what kind of bulb you have, but given the age of the vehicle, most of them have wire terminals that lend themselves to poking the meter's probe into the socket to get the readings. You already found the 12 volts on the blue wire, and that one CAN be measured with the bulb not in the socket. That's like taking the measurement at the faucet with the hose not connected. That one reading tells us everything up to that point is okay. The only thing left is the ground wire, but if we want to verify that, there's two ways to do it. One is by taking that second voltage reading with the bulb in the socket, and the other is by using the meter's ohm meter function to measure the continuity of the ground wire.