From my experiacne and this is going back 15+ years ago it was 16. But before all of that, you need experiance, you would need to know someone in the industry to get on any boat big or small charter, party boats or commercial boats.
Like i said this was 15+ years ago most charter boats only have a mate with 4 or more people,that usually is a family member.
The bigger boats have mates thats been fishing with them for years and years like a second family. Most wont give up their spot any way!
If you are serious about working on a boat, I would suggest going down the docks(all the docks) and start up a convo. and go from there! Cant hurt to ask, Good Luck to you hope you get your chance!