Can't say if you can use the circuit from your 3.6v (assuming the battery's where hooked up in parallel, is it a garden light perhaps?) unit, without knowing the parts inside. They may be rated to handle higher power they may not. Might not even need to handle power, just operate a relay, although I suspect a NPN transistor will be used (with an LDR as a voltage divider to activate) to do the switching.
If your multimeter has a 10A range and the panel only puts out 180ma, It should be safe to put red probe to + and black probe to - and see how many amps it makes. 200ma range should be safe to use, but if it goes over the range it will blow a fuse at best, and destroy the meter at worst (I've also had leads melt in my hands in under a second when measuring a current much higher than expected, so be careful, ask for help if unsure) Although I suspect your multimeter is not good or your using it wrong. As that panel should be making closer to 15v as you expected. As Cocacola said, The maths are not working.
Watts law says VxA=W so W/A=V and W/V=A
There is no way you can make the numbers in the advert work. it's a lie.
If you divide 1.55w by 0.18a (180ma) you get a 8.33333...volts. That's not going to charge a 12v car battery....
12v @ 180 gives you 2.16w
It just doesn't work out....
24v will charge a car battery, but it will shorten its life. Perhaps the panel puts out that much to allow for losses in the wire and connectors between panel and battery. The amp's and watts could be a guesstamate on what actually makes it to the battery. (p.s. Wouldn't you need to leave ignition on accessory for it to charge your car via cigarette plug?) Can you verify your multimeter by testing a few known voltages?
Why do you think that battery has a 1.5A max? If it is holds 4.5 amp hours as stated on the side it should be capable of putting out say 27amps for about 10 min. or 100ma for 45 hours. Depends what you plug in...... So no. Hooking a fan up and measuring current will just tell you what the fan draws.... Not total output of panel.Sounds like you have some more Googling and reading to do!
Make sure you understand how to measure amps!! doing it wrong can be dangerous. Even with that little battery! Put the leads straight to the terminals of a battery capable of putting out decent amps, and you will kill the meter every time! Possibly even start a fire.....
What a Charge controller (Like the one afa88 posted a link to) is monitor your battery and control charging and discharging of the battery. Which will seriously extend its lifespan, and in the case of lead acid, which produces hydrogen when charging (Lots of it when over charging), help prevent explosion!!... It will "trickle" down the charge current as the battery fills up. When you apply a load, it will disconnect it if you try and flatten the battery too low. I'd strongly advise getting one. Some of the flash models even have the ability to turn on a load when charge from panel stops(Like night lights, exactly what you want to do)....
As to the DC step down. I don't know heaps about them. But I would assume watts law applies. Almost all power converters change the volts and amps, while leaving watts almost the same. there is always a loss, sometimes more than others. you can expect anything up to about 95% of the watts in, to come out the other side in a different Amp to Volt ratio. Some systems can be very lossy. For example I was messing around with induction coils and stepping up voltage the other day. my system was only 17% efficient. So I was wasting 83% of my power...
Sounds like you have a lot to learn! I don't want to discourage you. Your project is fairly simple. It could be both fun and rewarding to make it work. If you want the easy way out. Just get a 6v solar charge controller with the ability to switch on a load in darkness.
MPPT's are more efficient. But I've never seen one that can do more than charge control. So no light switch. They tend to cost more too.
If you want to continue. First thing you need to do is make sure you can use that multimeter, then make sure it's working correctly and calibrated...
If Google is not making things clear. Ask here. there are ton's of people way smarter than me that work in the industry for a living, that come here to help people learn.
I'm also kind of curious about that panel. So I'd love to know what you find.
Good Luck
