In case you do visit Lushan again, it worth noting the hot spring “was” the namesake of the Seediq village Mhebu, which led one of the largest Aboriginal revolts against the Japanese.
I have read that Mhebu’s etymology (hmebuy∕mhebuy) in Seediq meant “leaky or air thick with water droplets”, referring to the steam from the hotspring filling up the air with water vapour that falls back down due to condensation.
That etymology along with the Mhe syllable probably resulted in the Japanese calling the place Musha (霧社), the village of fog.
It was only renamed to Lushan in the 1950s by Chiang Kai-shek who found the place very similar to Lushan in China. Lushan is a terrible name for the place. In a way it’s fitting that the hotspring town is now defunct. Perhaps the land can be returned to the Seediq people, and the place will be remembered by future generations by it’s real name, Mhebu.