What hours of the day will your 12hrs in Sasebo be?
Huis ten Bosch, the Dutch-themed theme park, is right there. Although the place does not seem to agree with some people's taste, I really love it there. You feel like you're in the Netherlands. It's fun to rent a bike and go on the canal cruise, and the night-time illumination is out of this world. Lots of fun games and activities, too. We were there for 10hrs, but anyways you'll want >5hrs there. It's ~1.5hr by train from Sasebo to Nagasaki each way, although unfortunately that train only runs hourly. It's actually possible to see Nagasaki in <3hr (trolley to Oura church, Glover Garden, walk back along Dutch Slope to Chinatown, back to station via trolley)... I've done this. It's not a complete tour of the city, but it gives you a good sense of what the city's all about. That might leave you ~5hrs for Huis ten Bosch. Well, okay it's tight. May not work out if your 12hrs in the wrong time of the day. Anyways, just throwing it out there.