I think the yellow wire is for voltage signal to alternator regulator, so is controls the voltage and charge output to the battery's. we used to get trucks that needed jump start for flat batts and if you didn't leave jump pack on for a bit the alternator wouldn't kick in and so the next time they stopped they would be still flat, i.e. no alt output.(this was in times before everything was controlled by electronics). i would connect it and keep a watch on battery's for overcharging, it may have been disconnected as a temp repair for a faulty regulator at some point. how long has this been happening, how long have you had the boat. if its only been used for days out and back on mains overnight the problem of no or low charge might not have been noticed.
you may be able to find a wiring diagram on here or google.