Brake/park lights

This would be typical of a poor ground. The clue is the parking lights will not light up at all if you press the brake pedal while the brake light bulbs are removed from their sockets. If the parking lights still do light up, check for a chewed up trailer harness. If you have a 7-pin trailer connector, check both sides of the terminals for built-up corrosion between two pins. Also, there was a pretty common problem in the '90s with 4-wire connectors that were installed by U-Haul. They had three red leds built into the connector to make it easier to identify the circuits. Sometimes those leds would short and would even melt the plug. The common symptom was the radio display would dim when you pressed the brake pedal because the voltage was back feeding into the running light circuit which also fed the dash lights.

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