A heavy dark gray base, some subtle noise and a 45-degree grid makes this look like a pattern with a tactile feel to it.
Source Atle Mo
Utilising some flowers from Almeidah. To get the unit tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Looks like a technical drawing board: small squares forming a nice grid.
Source We Are Pixel8
Imagine you zoomed in 1000X on some fabric. But then it turned out to be a skeleton!
Source Angelica
Inspired by a 1930s wallpaper pattern I saw on TV.
Source Firkin
Some rectangles, a bit of dust and grunge, plus a hint of concrete.
Source Atle Mo
This one needs to be used in small areas; you can see it repeat.
Source Luca
The tile for this is based on a repeating unit close to a design on Pixabay. It can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
This is the remix of an OCAL clipart called "Rain on Window" uploaded by "pagarmidna".Thanks.This is a seamless pattern of raindrops.
Source Yamachem
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Zero CC tileable seed texture, edited by me to be seamless from a Pixabay image. CC0
Source Sojan Janso
Not the most creative name, but it’s a good all-purpose light background.
Source Dmitry
One more updated pattern. Not really carbon fiber, but it’s the most popular pattern, so I’ll give you an extra choice.
Source Atle Mo
The image is a remix of "edo pattern-samekomon".I changed the color of dots from black to white and added BG in light-yellow.
Source Yamachem
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Clover with background for St. Patrick's Day. Add to a card with a doily, ribbon, a leprechaun or other embellishments.
Source BAJ
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin