This brings me to the question. Although a brain wallet doesn't make use of patterns, these seed phrases are stored in your head which is quite similar to what a border wallet does; so what makes it preferable to the Brain wallet if they both suffer the same disadvantages?
The assumption is that it is easier to memorize a pattern than it is to memorize a list of unrelated words, so a pattern can be more complex than a brain wallet, and this makes it harder to crack.
However, I think there are also disadvantages.
1. If you lose the grid, you have lost your wallet (unless you use the deterministic option).
2. The pattern is not random, so if an attacker gains access to the grid, it will much easier to brute force the phrase because there is a limited number of patterns that people will memorize. And just like passwords, some patterns will be used more than others. But, it would still be harder to crack than a brain wallet because it could be more complex.
...They want you generate a grid, write down its seed phrase, draw a pattern on that grid, remember that pattern, use that to generate a new grid, draw a new pattern on that grid, remember that pattern, and then use that to generate a wallet.
You have misunderstood the process. In short, you generate a grid of words, apply a memorized pattern to the grid, and then use the words in the pattern along with a memorized word as the seed phrase for your wallet.
If you don't want to store the grid itself, you can store a BIP-39 phrase that represents the grid instead. This option makes the process equivalent to using a BIP-39 seed phrase with a memorized pattern plus an additional word as a password. While more complicated, it is much more secure than storing a seed phrase and memorizing a passphrase.