The Republic of China took over Taiwan after the half-century Japanese occupation ended with the end of WW II. In 1949, the ROC was driven from the mainland to Taiwan in the Chinese Civil War. The capital of the ROC thus passed from Nanjing to Taipei under Chiang Kai-shek's rule. There was one political party, the Kuomintang, and the country developed under the martial law that already had existed earlier in the civil war, under the "Temporary Provisions Effective During the Period of Communist Rebellion." Martial law was in effect legally until 1987.
Today all that sounds that ancient history, but I was there in 1957, only 8 years later, when it wasn't ancient at all. There were a few ways that the political reality made itself felt. There were pictures of Chiang Kai-shek everywhere. One of the buildings at the start of our dirt road housed businesses and had hole-in-the-wall hovels in back where poor people lived. They cooked their meals and ate in the road, squatting around the fire. (I tried to learn that trick. Imagine not needing chairs, ever.) Behind and above them, always, the windowless wall of the building they lived in was wall-papered with dozens of identical posters of Chiang Kai-shek.
Military police directed traffic at all the busiest intersections. They all carried automatic rifles. My Mother and I were instructed to always be deferential to the Chinese, whether in uniform or not. There was a sense that the Kuomintang was insecure. They were trapped on an island and not sure they could even hold that. So there was a great deal of propaganda. In addition to posters there were speeches broadcast by loudspeakers around the city.
There were rumors of war. My Father confirmed nothing, but other children talked about military activities going on, such as shellings of off-shore islands. Some activities were evident but impossible to interpret, like the long convoys that would snake through the city, sometimes ROC convoys, sometimes US Army convoys.
The rumors of shelling may have just been out of date stories circulating about the First Taiwan Strait Crisis (1954-1955).
The US Army was expanding its role on the island, and that meant there needed to be good mess halls and servicemen's clubs. Over the Christmas break I was taken to such a club. My parents enjoyed a party while I and about a hundred other dependents were herded into a large ballroom to watch an American Western. Off to our right were windows maybe 6 feet high, for the length of the room, that had to be curtained during the movie. Before the curtains were drawn we had a view of a hole within which contractors were working to put a swimming pool.
Just before my Father left for the Mountain I found out that the swimming pool was what was keeping him at work late. He had discovered (surprise!) that graft was involved in its construction. The contractors were overcharging and my Father believed that Army officers who were supposed to monitor the contractors were taking bribes to look the other way. There were irregularities in accounting that appeared deliberate, and so forth. Dad was trying to get at who was responsible. There was fierce resistance and he was stressing out and drinking more, including after-work trips to bars with confidants.
My Father left for the Mountain right around Christmas. My Mother and I thought at the time that we wouldn't see him for the full six weeks, but just a week or 10 days later he was back in Taipei with a staff car to take us to the Mountain for a day, to see a USO show there.