Hi,
Any guesswork here would most likely cause a big problem. When it comes to charging batteries you can't mess around too much or things get really bad. Even lead acid batteries can blow up, and when they do they spew plastic and acid all over the place. Not something you want to have happen.
The only real way to know what is going on is to contact the manufacturer. They would know what they are for. There is another way, but it involves a lot of tedious work. You can trace out the PC board and draw a schematic. I've done this many times in the past and it works. If the parts are common, you can troubleshoot the entire circuit and find out if something is wrong as well as find out what the input/output connections do.
You are right in not connecting anything yet at the very least you could blow out the PC board and that would just make things worse.
I could give you some experiments to try but they would have to be done very very carefully so I do not thing it would be wise.
As another reader suggested, the battery voltage to charge a battery has to be quite a bit higher than the nominal voltage. If you have a 12v battery of
electric scooter, even the float charge is as high as 13.9v, and for two batteries in series that's already 27.8 volts which your output is not even close to yet.
However, there could be a problem with the batteries causing this also. You'd also have to test the batteries first.
Finally, charging two lead acid batteries in series is not really that great of an idea anyway. How do you control the voltage for each battery when the impedance of each one could vary wildly. The correct charge voltage to start would be at least 28 volts, and what if one gets 16v and the other gets 12v, that means only one charges. As they charge the apparent impedance gets higher or lower, and I do not think you can control the charge from just measuring the voltage across both batteries. Temperature differences between the two batteries is also an issue. You'd have to have a sense input for BOTH batteries. That's the right way to do it. That way the circuit knows the charge state of both batteries and can adjust the output to both batteries at the same time.
When it comes to charging batteries I always tell people to do it right. You can mess around with NiCd or NiMH cells but not with lead acid or lithium based cells. Very different. Why mess around anyway. If you want to charge them, you want them to charge the right way so they charge correctly and also have the life that they were designed to have.