I would get a small can of great stuff and try to fill the hole with that to give it a good solid back.
How to fix hole in wood panel wall.
Loosen the panel by lifting it from the bottom edge.
How to patch wall paneling.
How to patch a hole in wood paneling step 1.
Hold a hot steam iron against the damp cloth for about 30 seconds.
Cut a piece of panel slightly larger than the hole or gouge.
Tip if you are having trouble getting the wall patch to stick try wetting it slightly with a wet sponge or a using a spray bottle filled with water.
If the hole is only 6 wide a small piece of 2x4 or even 1x2 and a plywood patch will probably cover you.
Remove the wood moulding from the sides top and bottom of the damaged panel.
Scrape away loose debris from the hole.
Cut out a hole in 1 4 inch plywood or masonit adding about 1 2 inch or so on all sides.
A pry bar or screwdriver will work.
If you re filling a hole in a cabinet wall or a wardrobe place the craft sticks on the inside of the hole.
Use a utility knife to score an outline of the patch on the paneling surface.
Cover the hole or dent with fast drying spackle to bring the spackle level with the drywall surface and let it dry 24 hours or the time recommended by the manufacturer s instructions.
Cut some lumber to span the opening and attach it using screws through existing plywood around the opening.
Place the craft sticks on the back of the hole and secure them with wood glue.
When the great stuff was done.
Smooth the edges of the patch around the hole.
Measure the size of the defect in your project and add a little extra around it.
To seal the seams between your patch and existing plywood use wood filler.
Be careful not to.
Apply the sticky side of the wall hole patch around the edges of the hole leaving at least a on each side of the hole.
Cut the panel out.
Then cut your patch and mount it to the spanning pieces.
You should lay the craft sticks on the side they won t be seen from.
Press a damp cloth over the scratched area of the panel.
Take a utility knife and clean up the splinters on the edges.
Center the piece over the hole lining up grooves on the patch and paneling.
Be sure to use a large enough piece so that you can clamp this piece to the wood you want to work with and have enough room for the plunge router to move freely in the template.