The SL Hitoyoshi is a steam hauled excursion train operated by JR Kyushu and operates 1 round trip per day on weekends and Japanese national holidays from Kumamoto to Tosu and return. The train consists of 3 specially modified carriages which also include a sales counter, displays and lounge observation areas at each end of the train.
This train is fully covered by the Japan Rail Pass, all that is needed is a reserved seat ticket which can be obtained at a green ticket machine or ticket office at no additional cost but book early to get a good seat (or any seat for that matter).
I did travel on the train myself for the return trip from Tosu which has the diesel locomotive hauling the train with the SL at the rear. This was the only train that had seats on the 3 days I could do the train as I’d left booking till a day or so before.
Kumamoto City is also a nice stopover point with some nice attractions and can also be quite good for train spotting with a number of special trains departing this station, a longer video featuring these is coming soonish.