Pretend that you were a typical twenty-year-old Japanese-American male in 1942. Describe the circumstances in which you lived at that time. How would you respond to the American Army's request to volunteer for service in WWII?

While I can't answer this question by explaining things from the perspective of a twenty year old Japanese-American male in 1942, I can provide you with some background information so that you are able to.
As a twenty year old Japanese-American in the United States during 1942, it is very likely that you would be located somewhere in the western United States, probably along the Pacific Ocean. There is also a good chance that you would have experienced some degree of racism as you were growing up, and a good chance that it intensified following the bombing of Pearl Harbor.
Anti-Asian sentiment began with the arrival of Chinese immigrants in the mid-1800s. In 1882, the U.S. government even approved a Chinese immigration exclusion act to limit the amount of Chinese immigrants coming to the United States. What started as primarily anti-Chinese sentiment eventually developed into anti-Japanese sentiment as Japanese immigrants began arriving to the United States in greater numbers. In 1905, Japan defeated Russia in the Russo-Japanese War. This was the first time in modern history that an Asian nation defeated a Western nation. This caused fear amongst many Americans who believed that Japan could pose a potential military threat.
Americans also had a sense of fear regarding the success of Japanese immigrant farmers who had demonstrated success in growing crops in areas that had previously been considered unsuitable for farming. The increased fear led to increased discrimination against Japanese immigrants and Japanese-Americans.
In the aftermath of the bombing of Pearl Harbor, the American government and American people grew even more concerned with the presence of Japanese immigrants and Japanese-Americans in the United States. Within days of the bombing of Pearl Harbor, the U.S. government began detaining people of Japanese descent who they considered to be a threat to the nation. Oftentimes these individuals were Japanese community leaders. In many cases, there was no evidence provided that these individuals had acted in any way so as to create danger to the United States or to assist Japan. By the end of January, 1942, these individuals had been transferred to internment camps farther from the coast, often without notification being given to their families.
On February 19, 1942, President Franklin D. Roosevelt, signed Executive Order 9066. Executive Order 9066 allowed the U.S. military to ban individuals in certain designated areas. This order affected over 100,000 Japanese-Americans who would be forcibly removed from their homes in states along the Pacific Coast and placed in internment camps for the remainder of the war. Once in internment camps, Japanese internees were allowed to work, but they were not to be paid more than an army private. This certainly limited and reduced the economic standing of many Japanese-Americans.
Despite these conditions, there were thousands of Japanese-American men who volunteered for service in the U.S. military during World War II. A number of Japanese-Americans still felt a duty to serve the United States during the war. Other Japanese-Americans felt that by serving in the U.S. military during the war they would demonstrate to the American public that they were loyal Americans who were willing to fight and die for their country. They hoped to disprove myths that they were more loyal to Japan, or that they were an enemy within the United States. There are certainly more than a few Japanese-American WWII veterans who claim that their primary reason for service was to prove their loyalty to the government and American people. Many Japanese-Americans served the U.S. military not only in combat roles, but also in critical roles as translators and codebreakers against the Japanese military.
There were also quite a few Japanese-Americans who decided against serving the United States military. Their reasons for refusing to join included the fact that they wished to have their pre-war rights restored and the fear that they would be used in deadly missions in order to protect the lives of white members of the military.
As you can see, the situation for a young Japanese-American man during World War II would be a difficult one. There were certainly many conflicting feelings and emotions that led to the decision of whether or not to serve. I would argue that it depended a lot on individual values and decision-making that led one to either join the U.S. military or to refuse to do so.
https://www.history.com/topics/world-war-ii/japanese-american-relocation

https://www.pbs.org/thewar/at_war_democracy_japanese_american.htm