They can't burn themselves! That is one of the great features, no burns.
My Boaphiles had lights installed, but yes, drill holes for the cord and screws and mount it. I would use a small under the cabinet florescent type, they have covers and will be plenty bright. Cut the plug off so you only need a small hole then buy a snap on replacement. If your RHP didn't come that way the do the same.
Don't forget, the bulb will add a few degrees of heat, keep an eye on that...

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