5050 leds are 12v. So 8 AA. You may be able to get away with a single 9v. You usually have a few volts to play with.
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Or there is this option.
A single 9V will work, but not for a huge amount of time. The brightness becomes very important.
Most 5050 strands are 12 volt (8 batteries)but they may work on less. I would try 6 volt (4 batteries) to start and if not bright enough, then add more, do not go more than 12 volts (8 batteries) the length does not change the number of batteries, just the size. So the longer the strip the faster a Double A will drain.
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When I made a bunch of LED lit signs, I used these:
and:
Trim the LED strip to size and attach the barrel jack.
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Could be a solution:
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Have you considered putting three 18650s in series? Should be 11.something volts, with plenty of capacity and good recharge capability. 
I use 5v LED strips w/ USB jacks for all my signs… It gives the most options for power while still offering BRIGHT light. (Its also cheaper 
)
For example… 1m of 5v lights (~30 5050 led’s) actually made this lamp too bright.
All powered from a normal phone charging brick/jack or a portable USB battery pack.
https://www.amazon.com/gp/product/B012SMPY5I
I’ll post some pictures of 5v LED edge light signs when i get home (don’t have any pictures of them at work)
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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.
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There is one thing about LEDs not mentioned that is important.
Those LEDs require constant voltage. If it dips too low they go out.
So you need a buck-boost driver and the battery option will last longer.
otherwise those batteries will die over time as the voltage drops.
With a buck booster you can keep them going for a while longer.
Unless you like changing the batteries a lot.
Let me know if you want more info about these. I have made signs with custom drivers and control circuits.
In case your not aware of these buck-boost drivers here is an excerpt:
Buck-Boost LED drivers allow LED bias when the input voltage is either above or below the LED voltage. This is ideal in cases such as a single cell Li-Ion battery driving a single LED where the input voltage can vary from 4.2V fully charged down to 2.7V fully depleted while the LED forward voltage can vary from 2V to 4V depending on brightness and temperature. These LED drivers offer the highest efficiency, lowest noise, and the smallest footprints. Other features include integrated Schottky diodes, accurate LED current matching and multiple output capability.
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Here’s what I use for my signs if they are hard pressed for battery packs
https://www.amazon.com/gp/aw/d/B00JLY7L58/ref=mp_s_a_1_2?ie=UTF8&qid=1469152063&sr=8-2&pi=SX200_QL40&keywords=battery+pack+for+led+light+strip&dpPl=1&dpID=412gBL0nm9L&ref=plSrch
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No not really if you want them to shine bright like a diamond then yes but not generally required. I’ll have to do a video on how that’s done when I get time
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Looks awesome can’t wait to see so I can maybe incorporate it into my bases
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you can get on ebay and get 5 meter rolls of 12v leds for less than $5 a roll. they are out of china but are usually shipped fairly quickly. And they do not have the waterproof crap on them.
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I use those also and make sure you get the right connectors for them cause a lot of the on waterproof ones are to fat to fit in the connectors. that’s why I just buy the waterproof ones and just peel the crap off and glue it down
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seems pretty cool I don’t use rgb I’m thinking about it tho all mine are a one color design
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Could you please tell me your engraving settings? If its possible in metric
Thanks
