I've been travelling on foot and by hitchhiking and sleeping in a tent in many countries and now I'm doing so in Taiwan.
But in some countries it's really easy to keep fresh.
In Turkey I was often told I could wash with the taps for worshippers beside the prayer room or small mosque that many places including truck stops and petrol stations sometimes had.
In Thailand I would often meet people at a roadside restaurant and there was always a bucket shower they would point me to. Roadside police stations also offered me use of their showers, some of which were specifically public, and others I began asking permission to use.
In several Southeast Asian countries I've asked or had a local I met ask on my behalf if I could pitch my tent on the grounds of a Buddhist monastery/temple. I was always shown where there were showers or bucket showers.
In Japan and Korea there's always a sento or jjimjilbang where you can have a cheap and great bath and sauna.
In some countries showers were common in petrol stations or in public restrooms at parks and beaches.
I've even seen in some countries facilities provided for cyclists that include showers and walkers have also been welcome to use them.
So far in Taiwan I've made pretty miserable attempts to wash a little bit in public restrooms, but they're not common and often have a female attendant or cleaner, so you can't be very thorough. Until I move back from roughing it to hostelling.
Is there something I don't know about Taiwan that would be good for showering or similar? Hiking and cycling are very popular here. I don't know if people do those on overnight or multi-day trips. If they do there might be something they use.
Or are there any other ideas?