It's simple. Start a new empty layer and paint your pattern there. You can have a background layer under it to give a reference of the fabric color. I have only white here.
When you define the pattern (=have a selection, goto Edit > Define Pattern) for the forthcoming tiling, shut the background layer
The stamping result has no background.
But it can as well be watched with the background
ADD: The question has been radically edited. I assumed totally other problem. You can use layer masking to remove the white background.
- copy the image to the clipboard
- add a layer mask in the layers panel
- click the mask icon in the layers panel holding key Alt at the same time, you get the mask on screen for tweaks
- paste in place the image to the mask
- click once the image icon to see it, click again the mask icon to be able to make the mask ready
- goto Image > Adjustments > Curves. With it you can at the same time invert the mask to change white to black and find a good tresholding which removes the white background without trashing the image too much.
A dark test background layer is useful to see that the white really vanishes but the image is reasonably solid. A final, white test background should be used before making the stamp. Add them before all mask operations.
Inverting and tresholding:
Make the pattern stamp as described before:
Are you sure that you must do some background removal at all? For example subtractive CMYK printing can leave white out of the print automatically, because white is considered "insert nothing", other colors require ink to cover the paper or fabric. Maybe it's just now the right moment to ask the technical personnel of the print house.