The breather is disconnected from the air filter canister, and any other potential air leaks stopped as well, to ensure that the mixture is 100% controlled by the [former] manifold heat butterfly.
Regarding the mechanical fuel pump: On a carburetor engine, you will need to devise a way to stop the fuel at the jet. One thing to remember is that the float bowl will empty out more or less, causing a lean mixture, more or less, correspondingly. I don’t know if a PWM setup on an electric fuel pump will allow for much control in this situation.
The briggs V-twin that I worked with at Open Source Ecology had a handy solenoid for shutting off the fuel in an instant. That’s ultimately what you want, but I have no idea how to do that on an '89 corrolla.