That looks like a "lighting regulator".
If that is what it is (have one on my 15 horse) it was used to provide (somewhat) regulated 12 volt power to provide power for navigation lights "without" having a battery on board. It was an add-on for non-electric start models.
With the motor running at idle you get barely enough power to give a "dull glow" on a standard marine light bulb. With a bit of throttle there is sufficient power to light up an all round and forward nav lights.
You could check to see if it is still functional with a voltmeter/multi-meter - it should be producing about 12 volts DC. If it is not working it could be the regulator itself OR the charge stator which was is separate from the ignition stator (add on unit in non-electric start models) that has gone bad. Unlike a "rectifier" which is used to charge a battery, the regulator (originally called a lighting regulator) will not "kill itself" if it is not connected downstream to a battery or lights.
If it is shot it can be replaced with part number 95845T (voltage regulator). It is listed as No Longer Available (NLA) but a number are still floating around and list for about 100 bucks.
edit to add - this will NOT charge a battery. You would need to replace it with a rectifier AND always have a battery attached when the motor is running. The charge stator on these puts out a max of 4 amps, so will keep a starting battery "topped up" but if the wish was to replenish a deep cycle battery that was used for electronics or a trolling motor, it would take 20 hours running at max throttle to recharge an almost fully discharged group 24 deep cycle - so not practical for that purpose at all...