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Can't really charge one battery from another. The charging voltage to charge a regular 12 volt battery is 13.8-14.2 volts.Lithium battery chargers need around 15 volts from the charger to get a full charge if I remember correctly.In order to charge from another 12 volt battery get a small 115 volt inverter and use your lithium batteries charger to charge it.
I think I confused people...I have a amped outdoors 12 volt 10 amp on my sonar. I also have an amped outdoors 12 volt 60 AH battery I use for my trolling motor in the summer. I was trying to see if the 10 ah ran out on a 2 day trip could I somehow charge the 10 ah with either the 60 ah or with my battery box that has a 12 ah in it and a cigerette output plug?
The lithium batteries take a slightly higher voltage to charge to 100% than Lead/acid. I was told by my battery supplier than I could use my 12V charger on the "AGM" setting, but the battery never got to the specified "full" voltage. I ended up buying a LIPO4 specific charger, and it works better and faster. That said, if you connect the 2 batteries, my guess is that they would equalize, and the small battery would have the same voltage as the big battery. My biggest concern with this is that there is no protection for max current or for temperature, so you might cause damage. Your best bet is to rig a harness to use the trolling motor battery to power the flasher directly. That is cheaper and safer. If you don't want to do that, 18V tool batteries can be used to power most 12V electronics. Most people have multiple of those.