1. Check the Bulbs:
* Obvious First Step: Replace the driver's side brake light bulb. Even if it *looks* okay, it could be burnt out or have a weak filament. While you're at it, replace the passenger side bulb as well for consistency. These are likely single-filament bulbs for brake lights only (they won't have a running light filament).
2. Inspect the Bulbs and Sockets:
* Filament Integrity: Carefully examine the old bulbs. If the filament is broken, you've found your problem.
* Socket Contact: Look for corrosion or damage within the bulb socket. Clean the contacts with a wire brush or sandpaper. Make sure the bulb makes good contact with the socket.
3. Check the Wiring:
* Wiring Harness: This is the most likely culprit. Locate the wiring harness for the brake lights. It'll likely run along the frame or under the car near the taillights. Visually inspect it for any breaks, chafing, or corrosion, particularly near the driver's side.
* Connections: Check all the connectors and splices along the harness for secure and clean connections. Corrosion can disrupt the electrical flow. Disconnect and reconnect each connection to ensure good contact.
* Ground: A bad ground is a common cause of electrical problems. The ground wire for the taillights should be connected to the car body near the taillight assembly. Clean this connection thoroughly.
4. Test with a Multimeter (Best Approach):
* Continuity Test: A multimeter is essential for a definitive diagnosis. You'll need to test continuity in the wiring circuit.
* Turn on your brake lights.
* Set your multimeter to the continuity setting (usually represented by a diode symbol).
* Probe the wiring harness connectors at the taillight. Check for continuity between the brake light wire at the driver's side socket and the appropriate wire at the brake light switch. You should have continuity *only* when the brake pedal is depressed. If you don't, there's a break in the wiring somewhere.
* Repeat the test for the passenger side (should show continuity). This helps verify the overall circuit is working.
* Voltage Test:
* Set your multimeter to measure DC voltage.
* With the brake pedal pressed, test the voltage at the driver's side bulb socket. You should see battery voltage (around 12 volts). If not, the problem is upstream of the bulb.
5. Brake Light Switch:
* Switch Operation: The brake light switch is located near the brake pedal. It's a simple switch that closes when you press the pedal. Test its operation. A simple continuity test with the multimeter should verify its operation. If the switch is faulty, it needs to be replaced.
Specific to a 1964 Impala:
* Wiring Diagrams: Find a wiring diagram specific to your 1964 Impala. These are invaluable for tracing the wiring paths. You can find them online through various sources (e.g., classic car forums, online parts suppliers).
* Grounding Issues: Older cars can have significant grounding issues. Poor grounding can cause intermittent or complete failure of lighting circuits.
If you're not comfortable working with car electrical systems, take your Impala to a mechanic specializing in classic cars. Working on the electrical system requires caution; incorrect wiring can damage the car's electrical components or even pose a fire hazard.