Dealing with emergency situations in Taiwan

Dealing with emergencies in Taiwan is in theory like that in most places, and would vary depending on the specific location and type of incident.
Medical issues calling for immediate care would be a problem in remote places due to lack of nearby facilities.
Always be wary when travelling to rural or alpine locations.
Most medical emergencies can be looked after in the major cities with availability of larger hospitals, albeit English-fluent staff may be hard to find.
Being vigilant, well-informed and sensible is the best way to prevent emergencies.
For example stay away from interior, alpine locations during and after downpours, quakes would prevent being caught in landslide.

Years ago I had an emergency need for spinal surgery to correct a burst spinal disc that caused acute sciatica, an extremely painful condition I'd researched and was 99% sure of its remedy. But this female doctor at the Zhen-Shin Hospital saw me on one of the better days when I could still walk, so refused to prescribe an MRI and surgery. Then I had to suffer 4 more weeks of excruciating pain before seeing a male doctor who right away operated to have saved me from nightmarish pain.

The lesson is you sometimes have to be lucky to meet the right doctor with less attitude and more humility.

Also be wary of doctors as orthopedist who runs a rehab clinic. He or she cares more about steady income than your spinal and skeletal pain that may not be improved with whatever rehab equipment available in the clinic. In short he/she will routinely prescribe rehab to keep you as paying customer regardless of effective treatment.

Note also that many doctors in major hospitals in Taiwan (as internist/orthopedist/neurosurgeons) book 50-plus patients daily due to pressure to generate income, hence only giving each patient maybe 2 or 3 min. of time. Expecting personal, proper attention therefore is about as realistic as expecting to find snow in Death Valley.