Hello,
Your clock was made in the early to mid 1980's and has a Korean made movement. Your type of clock typically had the case made in the United States with imported Korean or Chinese made 31-day movements and could be had from J C Penney and Sears Catalogs. I DO NOT recommend working on the clock or trying to wind it if the click is broken! The Open-style springs in these clocks are so powerful that even most clock repair professionals will not work on them. I would suggest you purchase a replacement movement from Merritts
31 Day Korean Mvt (Giant) on Merritts.com
The price of a replacement movement is far less expensive than trying to find parts and/or the expense of having a repair person work on it.