I deleted my previous post since I didn’t read the original post correctly. I read 12x18 and assumed lights were going around the whole thing. But since it’s just a 12" LED strip that you need to light, then you can easily get away with a small battery pack.
If you use 5050 60LED/meter strip, then your 12" strip will pull about 0.4A, or so. A 4Ah battery pack would last a good 10 hours at that rate. DanBrown’s suggestion of using 18650 cells would work well. Don’t buy cheap ones, though. Some of the cells you can get on eBay are literally fake.