The new --proxy option in Sauce Connect version '3.0-r28, build 43' enables the use of BrowserMob proxy with Sauce Labs. To make this work, a BrowserMob proxy connection is established, then Sauce Connect tunnels are set up using specific flags, including `--proxy`, `tunnel-identifier`, and `readyfile`. The browser is then launched using the right tunnel identifier, followed by manipulation of the BrowserMob proxy to perform tasks such as basic authentication. Once done, the tunnel is closed, and the sauce connect process is shut down. This allows for efficient automation testing with the BrowserMob proxy on Sauce Labs.