Yaris 1.0 T-Spirit (2005): tail/brake light puzzle

[MichaelFr]

The left tail light and brake light work individually but both cut out when used together:

- when lights are off, the brake light works

- when lights are on the tail light works.

- when the lights are on AND I apply the brake both cut out.

Any ideas what’s going on and how to fix it? Many thanks.