93 lexus gs300 charging system not working after new alternator why?

There is a lot going on here.

Your electrical system relies on proper connections to the positive and negative poles on the battery. The positive wires are pretty obvious, since each one goes to the device it is to power, like the starter or headlights.

The negative, or ground, side of the system isn't quite so obvious since it often uses the major metal parts of the car in place of actual wires. Sometimes those wires get accidentally removed or broken.

The car dying when the brakes are applied, is just from the battery being discharged. There isn't enough current to run the engine and brake lights.

If you have a volt meter, the voltage of a good battery with the car turned off will be about 12 to 12.5 volts. With the car running, that voltage will be above 13 volts, and about 14 volts on a fully charged battery. If you measure anything less than 10 volts on the battery, it's life is is being reduced.

I would start by checking the ground system, since missing ground wires cause various circuits to seek that ground connection through other devices. In this case anything can happen!

With the volt meter and the car running, put the red lead from the meter on the positive on the battery, and then, with the black lead on the meter, touch a clean metal area on the engine. you should read above 13 volts. Touch the body with the black lead as well. This should also read above 13 volts. Anything less means the ground circuit is faulty.

There will be a large wire from the battery negative (-) terminal to the engine somewhere. There will be a wire to the body probably from the battery negative to the body, but also from the engine to the body. In computer controlled cars, these grounds are extremely important. If you look closely, you will see groups of wires together to a bolt on the body. these will go to various points in the wiring loom. All these connections must be present, clean, and tight.

Less likely, is that modern cars often have the alternator voltage controlled by the ECU or engine computer. If that is the case, the battery can discharge or even overcharge. This situation would not explain the odd tach reading.

That's my best shot with the info given.

Good luck