Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
A bit like some carbon, or knitted netting if you will.
Source Anna Litvinuk
Derived from an image that was uploaded to Pixabay by darkmoon1968
Source Firkin
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
Prismatic Groovy Concentric Background 2
Source GDJ
Sort of like the back of a wooden board. Light, subtle, and stylish, just the way we like it!
Source Nikolalek
From a drawing in 'Studies for Stories', Jean Ingelow, 1864.
Source Firkin
As far as fabric patterns goes, this is quite crisp.
Source Heliodor Jalba
Prismatic Curved Diamond Pattern 5 No Background
Source GDJ
This is a semi-dark pattern, sort of linen-y.
Source Sagive SEO
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A dark one with geometric shapes and dotted lines.
Source Mohawk Studios
We have some linen patterns here, but none that are stressed. Until now.
Source Jordan Pittman
Just the symbols of the signs of the zodiac distributed in a chequer board-like pattern
Source Firkin
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i
Source Firkin
Black version of a pattern that came out of playing with the 'light rays' plug-in for Paint.net
Source Firkin
Prismatic Polka Dots 3 No Background
Source GDJ
A large (588x375px) sand-colored pattern for your ever-growing collection. Shrink at will.
Source Alex Tapein
You were craving more leather, so I whipped this up by scanning a leather jacket.
Source Atle Mo
A background pattern inspired by designs seen in 'Burghley. The Life of William Cecil', William Charlton, 1857.
Source Firkin
A seamless pattern from a tile made from a jpg on Pixabay. To get the tile select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Drawn in Paint.net using the kaleidoscope plug-in and vectorised.
Source Firkin
To get the tile this is formed from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
This was formed by distorting an image of a background on Pixabay.
Source Firkin
A slightly more textured pattern, medium gray. A bit like a potato sack?
Source Bilal Ketab
Adapted from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin