I looked into magnets for the lamp base, but tried "VHB tape" which is a double sided foam tape. After cleaning the base of the lamp and bullet tray with alcohol, it stuck firmly! I was kinda surprised how well it's stuck. The black switch on the back of the base is also stuck on with VHB tape, as are a couple of wires. I assumed I'd have to figure out how to use screws or magnets later, but this thing is on there for ever. GWStar's magnetic LED tape is a great idea too -- just be sure to actuate your press slowly and make sure there's clearance! The LED tape came with a sticky backing, which is holding so far, but i'll use magnets if it fails.
white stuff on bullet tray is just some foam to keep soft bullets from denting as drop them on the tray. probably not necessary.
For the electricians here, I measured the current too. the 12 LED's on the tape burn 145mA, and the flex-lamp pulls 161mA. At 12 volts, that's 4 watts, which is well under the adapter's 6watt rating.
Building this wasn't hard, but sourcing the parts can be tricky -- keep the sources of these things coming! Most of the heche-en-china parts don't exist for long.
--edfardos