I've left the covering on some of mine before. Aluminum tape works fine but you will need to change it every time you take the pad off for cleaning and I think it is pretty expensive. I use it for my already-used UTH's on different enclosures and on my flexwatt.
As for placement, I would put it on the bottom of the tank, not the side (if that's what you're asking). The reason for this is because it will be more efficient in heating your snake for 2 reasons:
1. It will directly heat the stomach region to aid in digestion
2. It will heat the substrate. Glass is not a good conductor of heat and generally, substrates are much better than glass. Therefore, the heat will spread into the substrate and warm a bigger area and make a large warm spot instead of a small hot spot, which can hurt the snake.