Ok, I dug out the starter charger I bought a few years back and had a look at it for running 12V LEDs.
Here is the box and it claims 26Ah:
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This is what's in the box. The charger/starter unit itself, a wall charger, a load of adaptors and some crock clips for connecting to a car battery. This model has extra functions, like being able to switch the charger output from 5V to 20V, so you can even run laptops from it:
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I have never actually used it in anger to try and start a car. The one time I had a flat battery and I tried to use it, nothing happened. I later realised that the thick wire soldered to the reverse polarity protection diodes on the positive lead had become detached, hence no power was output. Oh, the joys of lead free solder...
So let's open it up and have a look. A fair bit of electronics and a battery pack of, wait for it, 3.8 Ah!! The 11.1V nominal suggests 3 cells at 3.7V. Probably LiPos in that shrinkwrap. The OCV was 12.4V from the 12V starter socket. The entire unit weighed about 400g.
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So let's connect it to a 12V LED lamp. I bought this LED lamp a while ago. It's for attaching to cars to add extra driving lights. It runs at 1.5 A at 12V, so 18W. I like the housing as it has a decent heatsink to keep it cool:
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I charged the starter/charger to 100% and I inserted the croc clips cable into the car starter socket on the unit. Then I connected them to the LED lamp:
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I let it run for 1hr and 40 min. The charge indicator went from 100% to 35% in that time. Voltage output dropped to 11.1V and the current was just over an amp.
I expect this particular unit could power this LED for a couple of hours. This would be fine for me, most of my journeys are far less than an hour. However, I decided against using it as it is a bit bulky for what I need, with all the extra stuff on it for supporting lots of charging output options.
In summary, I think these units have some utility for running 12V ancillary equipment on e-bikes, as an "off the shelf, contained solution", but just don't believe the quoted Ah values at all! However, if you are comfortable with building your own battery pack, I think that would be the optimal solution.
If you do use one of these, I do think it is a good idea to put an inline fuse in the output for safety.