If you try the "Make seamless" plug-in in GIMP, it will make the image seamless both horizontally and vertically at the same time. It will not allow you to make it seamless in only one dimension.
This instructable will help you to make images seamless in only the dimension of your choice.
Step 1: Open the image in GIMP .
(Lets call the default layer the "base")
Step 2: Select and copy the left 1/3rd of the "base" layer.
Step 3: Paste it in a new transparent layer
Let us call the new layer "left on right".
Make sure you paste at the right 1/3rd of the image.
Step 4: Select and copy the right 1/3rd of the "base" layer.
Step 5: Paste it in a new transparent layer
Let us call it "right on left". Make sure you paste it at the left 1/3rd of the image.
Step 6: Add white layer masks to both the new layers.
Step 7: Blending the masks. Step1
Select the "blend" tool - use the "Foreground to background" gradient, linear blend mode.
(make sure the 2 colors are black and white)
Step 8: Blending the masks. Step2
On the layer mask of "right on left" layer, draw a gradient from exactly 1/3rd of the image, all the way to the left boundary of the image.
Step 9: Blending the masks. Step3
On the layer mask of "left on right" layer, draw a gradient from exactly 2/3rd of the image, all the way to the rightmost boundary of the image.( or you can also copy "right on left"'s mask and paste it on "left to right"'s mask and flip it horizontally)
Step 10: Crop away 1/6th of the image from left and right each
Step 11: Testing & Finish
With these, the image will now be seamless horizontally, retaining the nature of the image vertically.
To test, use the "tile" plug-in. It is at various places in different versions. So i wont instruct on how to use it.
These instructions were for making an image seamless horizontally. You can adapt them to make images seamless vertically only too.