A seamless pattern of dark bricks. Maybe it's not very realistic, but it looks good in my opinion.
Source V. Hartikainen
From a drawing of the coat of arms of the Ottoman Empire on Wikimedia.
Source Firkin
From a drawing in 'In an Enchanted Island', William Mallock, 1892.
Source Firkin
Prismatic Geometric Tessellation Pattern 4 No Background
Source GDJ
This is a hot one. Small, sharp and unique.
Source GraphicsWall
Simple gray checkered lines, in light tones.
Source Radosław Rzepecki
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
A nice looking light gray background pattern with diagonal stripes.
Source V. Hartikainen
A seamless dark leather-like background texture with diagonal lines that look like stitches.
Source V. Hartikainen
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
Alternative colour scheme. Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
"Beige Stone", Tileable Texture.
Source V. Hartikainen