Upon graduating from high school, Kawamoto was first employed in the making and designing of precision machinery. During this early period, he became interested in becoming an animator due to the ongoing Macross series, Yoshiyuki Tomino's Mobile Suit Gundam and Gainax's amateur Daicon films. In particular, Yoshikazu Yasuhiko's work was a major influence.
After graduating, he applied for a small sub-contracting studio called Group Donguri and was accepted. In 1986, he made his debut in Yasuhiko's 1986 film Arion. During the production he was mentored by the character designer Sachiko Kamimura, with whom he would later work with on multiple occasions, including being her assistant in Venus Wars, which was also written and directed by Yasuhiko. After this Kawamoto worked on numerous series by Sunrise, most notably as a character designer on the Gundam entries, Stardust Memory and The 08th MS Team, as well as the internationally acclaimed Cowboy Bebop.