Both brake lights do not work

Welcome to 2CarPros.

Often times, you will see 12v with a multi-meter, but when any real load is placed on a circuit, it can fail. With that, I need you to go back to the switch. Put the brake light bulbs in. Test for 12v in to the switch light green/red wire and with the bulbs in, check for 12v out (light green wire) when you actuate the switch (see picture 1). If that fails or shows a drop in voltage, then we know the problem is either the switch, the relay, or the relay ground.

If it fails, check the brake light relay ground, See picture 2. Check it for corrosion, damage, and make sure it is tight and clean.

If the ground is good, then we need to check the brake light relay. (picture 2) Here is a link to help with checking a relay:

https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit

Here are a few links you may find helpful:

https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester

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

https://www.2carpros.com/articles/how-to-check-wiring

Let me know if this helps or if you have other questions.

Take care,
Joe