It is confusing logically because vivo is a characteristic that is stronger and more enduring than brillante, yet brillante uses ser... this is one of those situations to memorize. Vivo uses estar. Maybe there is a difference between being alive physically and being alive inside (emotionally)... I'm not sure. I will use estar for alive and dead
It wouldn't be confusing if we put it in our minds that ser is for characteristic and estar is for state. Being alive/dead is not a characteristic but a state, just like with fruits being ripe/unripe, regardless of permanence or being temporary.
Being kind, good, bad, brilliant, dull, tall, short, boring, etc. is characteristic.
Being ripe/unripe (fruit), sick, well, dead, alive, bored, angry, etc. is state.
[Spoiler alert] Unfortunately for the ducks, we later learn that they are injued (“Los patos están heridos” - “Participle” lesson). Our narrator firmly asserts that they will never eat duck (“Yo jamás comeré pato” - “Future Tense” lesson) but later seems to have a complete change of heart (“Me gustaría comer pato“ and “Quiero tener dos patos” - “Conditional” lesson).
Ahora, el pato,
(preparado sin glutamato)
está en un plato.