I can remember the rare few occasions that call for an early rise, they usually involve catching a plane, or getting to a dive spot in fairly distant location.
But in Alishan, sunrise watching is a big thing for tourists. And often visitors would travel between mountains in the wee hours just to catch a glimpse of the first light of dawn.
On my first trip, I went to two sunrise watching. First being the less visited Yu-Shan that's the next mountain away which requires a booking on a tour van to get to, which meant departing from my hotel at 4am in the morning; the second was taking the 'small train' 小火车 up to the peak of Alishan to catch sunrise (which I did on the last day of my stay.
My visit to Yu-Shan was an uneventful one, having the foggy morning didn't help. It was too cold and too early. Turned out we could neither see the sun nor get a refund on the wasted journey. It's always a gamble on trips such as these. But the view has more than made up for it, or so I comfort myself with.
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Between you and me, the trip's worth a shot as there's rarely anything to do in the mountain (no bars, etc) and you usually get to bed pretty early, leaving you wide awake by 4am. It doesn't cost much and you did travel, assumingly, to Alishan to immerse yourself in nature and the park doesn't open till after 8am-ish which you would be back in your hotel by then.
I did manage, however, to see a 2700 year-old cypress tree 鹿林神木 with an impressively wide trunk.