To convince young Emmett to construct the drill, after you called him from the soup kitchen and went by the court house, talk to him until he only has 2 questions left to ask, causing repetitive responses. Go to the jail and talk to Doc about his younger self. Then use the tape recorder on young Emmett. Play the tape for Doc and he will solve the problem. Go back to young Emmett and give him the solution. Through the dialogue you convince Emmett to build the drill and you're set up for the next quest.