How can i make a snake following my player without any lag, when moving on a grid?

I kinda did some of that but not shown in my screenshots. Each segments of snake has an Index variable. Head being 1, First part being 2, and so on.

On a previous version, was able to generate parts, but… visual wasn’t … good.

What i don’t get at all, isn’t that, it’s truly that movement. Should i keep my idea of top down behavior on player, and each Snake Part? Or is there other way?