I'm not a boater yet (let's just say that immediately
) But it sounds like the switch to me or a dry earth. Easiest fix first is clean off the battery terminals and rough up the connectors, reattach then try. If it's not that the switch (or the connectors to it) may be also dry earthed. Is the switch on the side of the throttle? If so, is it something that can be popped out?
In car components (where I'm currently more comfortable) electrical components rarely 'half' work. They're either knackered, or not. I'm sure the tilt mechanism (an electric motor) is much the same.