Here are the main components available in one or two days from Amazon. I used 3/4" Baltic birch plywood and a 1-1/8" dowel purchased at Home Depot. You will need a couple of connectors to terminate the supplied cable to the battery. They crimp on and then I used heat shrink slipped over the connectors. Hers has four rubber feet.
The unit is not light, but if moved near the person's bed I could stay there and be plugged in there nicely.
When building the box please be mindful that the battery has to fit inside when you complete your work. My design put a priority on making the handle secure, it has 1" of plywood above it, it is glued in place and there is a screw that was run through the plywood and into the dowel. Be sure to drill the plywood wide enough that the screw slides in and out without effort. Use a smaller drill for where the screw hits the dowel. To that end, the bottom screws in place with six drywall screws. To change batteries you unscrew the bottom, slide out the old and slide in the new. Mine is three years old and humming along nicely.
Be sure to buy sealed, AGM batteries for safety - they can work upside down!