Ok so I've been playing through emerald again and I'm trying to get a shiny Rayquaza. I've been turning off and on for a couple days now. I'm wondering at what point does the game decide that the character will be shiny or not and wouold the overworld sprite be shiny also?

Generations III and IV
In Generation III, most of the data structures were redone. As such, a Pokémon's shininess would no longer need to be linked to its stats due to incompatibilities between the previous generations. The determinant for shininess is instead a calculation based on the Trainer ID number and secret ID number of the player encountering it and the personality value of the Pokémon. The same method is used in Generation IV.
The secret ID and Trainer ID bytewords are first xored together, and then the first byteword of the personality value is xored with the second byteword of the personality value. If the xor of these two results is less than eight, then the Pokémon is Shiny. This results in a probability of 8 in 65536; simplified as 1/8192 (2-13, or approximately 0.012207%), just as in Generation II

Basically what this means is you always have a 1/8192 chance that it will be shiny.

Unless you want to RNG Abuse for Shiny Rayquaza, you will be resetting for many more days.

I'm fairly certain the overworld sprite will never be shiny. The odds for catching any shiny pokemon are 1 in 8192. The game never "decides" if a pokemon is going to be shiny, it's a matter of luck. My advice: don't go shiny hunting, just have fun and play the game.

I've already beaten the game several times, the entire goal of this file was to try and get the shiny ^^;

I remember I once did the exact same thing, only to get it shiny first try! Don't give up man, it'll be worth it