I've personally tried the following battery combinations. I first started tests with the tubelight using standard Li Ion rechargeable batteries purchased via Ebay.  I do not recommend buying them as they are generally of low quality and will fail in short time.   The sellers are  in China and will not back their products.   These Li Ion batteries come with their own chargers and are usually set up with the US plug style, but will operate on 110-220V and 50-60 Hz.      The seller will usually provide an adapter for your country.     The adapter I received for Germany would not fit in the German wall outlet.   The German wall outlets are round and the plug sent was not round.  

I bought two of these battery packs from "reseller-channel".   It was advertised as 12.6V and 1800 mah.   It cost about 12 EUR including shipping.     The battery never drove the lamp for more than 80 minutes, which would mean a capacity of 900 mah.  With every charge the run time was reduced.   Within 5 uses the battery was dead.    The seller assured me of a replacement but it never was sent.   He delayed and delayed until the 90 day Ebay dispute resolution time was over, so he would not get negative feedback.   It was wasted money.

There are many people on Ebay selling the same battery for CCTV's.    The 1800 mah battery in a plastic housing is junk and you will only be disappointed if you buy it. 

More and more I see these Li Ion batteries from Yingshibao Technology Ltd. packaged in blue plastic foil on Ebay.  They are not really packaged well to take abuse (vibration and shock).   There are three plate like cells all soldered together at the top of the battery by the connectors, and shrink wrapped in a hard blue plastic foil.  The batteries come with a male and female 5.5 x 2.1 mm connector so adapting to them is easy.    The batteries I have seen recently, come in 4800, 6500, and 9800 mah capacities.   They also come with a small and compact 110-220 50/60 Hz charger.  The charger has the plug for type for North America, so you would need an adapter for Europe or other places.  As far as the cost goes, you can't beat the prices if you can believe the capacity ratings.    The 9800 mah battery could in theory run an Alien Eye lights for almost 17 hours before recharging.   I have used the 4800 mah battery.  It fits perfectly in the handlebar bag, but twice it stopped working prematurely after a couple of hours in a test ride on the road bike. I suspect the hollow connctor was shorting out on the lamp connector.  (see troubleshooting)   It only gives me about  2500 mah now before I have to recharge it       I carry it in a backpack driving a helmet light.   I like how it works.  A backpack is a much more cushioned and shock isolated place compared to under the handle bar.   So in the case of sellers in Hong Kong, it is buyer beware.   Here are my tips if you want to risk buying one of these batteries.

1.   Read only the seller's negative feedback to see how he works.  I'm sure for every negavtie feedback they have there are at least a dozen other unhappy people for similar reasons who did not get their feedback registered in time.  Only buy from a seller who sends with registered mail.   Write them if you are unsure.  A common complaint from customers buying from  Hong Kong sellers is that the goods never arrive.   It has happened to me.

2.  When you pay with Paypal, make sure you use your credit card and not from funds in your Paypal account.   You get extra protection with your credit card that you do not get from Paypal on problem purchases.   If Paypal will not cover the lose, then report the problem to your credit card company.    You might have to drain your Paypal balance in order to not have Paypal use your cash funds first. 

3.   If you have a problem with the buyer, register a formal complaint in Ebay or Paypal right away.   Even if the seller gives you assurance he will take care of it, file a claim anyway.   One game they have is to lead you along until your time to file a complaint runs out, and then they are off the hook.  You will not hear from them again.  I learned the hard way on this one too.

4.  Take care to protect the battery, especially the end where the cable comes out.  The wrong pressure in the wrong place and the battery can cut off on you.   If the battery cuts of, plug it in the charger.  I have the feeling this can reset the error with the battery.

5.  You might have to pay customs duties on the more expensive batteries depending on what the seller includes for an invoice with the package.

Here is a list of sellers on Ebay who I see selling such batteries:   Summary from Ebay shops .com   Ebay shops .de

Li Ion versus standard NiMh (akkus):

The Li Ion batteries generally have a much better power to weight ratio.     The Li Ion have individual charging systems that are usually not transferable from one battery to another, so if the charger dies, then you might need to buy a new battery just to get a charger.   According to Wikipedia, the typical Li Ion battery will lose 20% of its capacity per year due to aging, although the typical NiMh battery will probably be dead in a year with frequent use.  It is important not to use fast chargers using a rate over 500ma as they significantly reduce the battery life.  

I decided to use the standard NiMh Akkus since they were in my opinion more robust.     In Germany you can get a four pack for 2.99 EUR at  Aldi when they run their specials one or two times per year.