It depends on what kind of relay you are using. For a standard automotive relay (such as Bosch) you can do it with a single SPDT relay.
In the diagram, when the brake lights are on the relay will close and the LED will be powered from Switched +12V through the normally open contact (87). When the brake lights are off the LED is connected to the manual switch through the normally closed contact (87A).
So when the manual switch is closed the LED will light with the brakes either off or on.
You have to be mindful of the relay coil contacts, some have a built in diode so are polarity sensitive, typically you put the positive of the trigger voltage to 86.
Here's a diagram of a relay with a diode, not that positive should go to 86, negative to 85.
Some relays have a resistor instead of a diode, some don't have either, these types are not polarity sensitive but it's best to follow the polarity convention in case someone comes along later and replaces it with one that does have a diode.
Note that this circuit will only activate the LED with the manual switch. If you want to activate the existing brake lights as well it depends on how the brake lights work, if they have one side grounded and the other side switched hot you can use the circuit from MOSFET's answer, if they're ground side switched it's more complicated.
simulate this circuit – Schematic created using CircuitLab