You probably have a Honda 9.9 with a magneto, if it's an outboard. I have a Harley AGM deep cycle that I use for nav lights in my Zodiac that is powered from this, and I have been quite happy with it. It is about the size of two bricks and is bungeed to the fuel tank. A pair of 12 ga wires with an inline fuse charges the battery, and I don't charge when I'm going full out, because the magneto produces more voltage (about 20 VDC) than I am convinced is good for the battery.
It gives me a red-green at the bow and a white stern light on a stick for two or three hours with the engine off. With the engine on, I can run a small spotlight to show logs and branches ahead of me when I bomb around in the middle of the night south of Toronto Island. Yes, my insomnia cures are many and odd.
The best part is that the AGM is light enough to haul home on a bicycle, where a monthly session on a trickle charger keeps it happy all winter.
Is that battery an Optima knock-off? Just curious if they make it or if it is made for them.