OK. I'm looking at your picture.
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You are wanting to attach these cardboard tubes to the under side of your play field. I agree with Darcy, replace the cardboard with plastic tubes. I think you could find the right diameter in PVC plumbing tubing. For what you are doing, hot glue should hold those tubes securely enough to the play field. Hot glue would be a temporary bond that can be broken with a hair dryer.
I'm 95% positive that the type of plastic the play field is made of is bondable and will accept Superglue. So you could bond either cardboard tubes or plastic PVC tubing to the play field in a permanent bond using superglue. But hot glue has good holding power and gives you the flexibility of a temporary bond.
If you wish to take it a little farther, you could bond a a small flat piece of plastic to the side of the plastic tubes; This would make a mount to which you could use a standard bayonet light bulb socket. You can buy bayonet sockets in all kinds of configurations for any type of mounting situation. The metal tabs on these sockets bends into any shape of angle easily. You could make the bulb fit into a plastic tube at any depth you would want and be able to get rid of that squeeze type socket if you wanted to.
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