Kaiserslautern is a town in Rhineland-Palatinate and is famous for football. Most major roads in the city are two-laned and without free space at the edge which makes finding a good hitchhiking spot difficult.
West (Mannheim, Ludwigshafen)
There is a bicycle path on the Mainzer Straße leading to the highway. You might be successful there but be careful that the car won't cause a crash with a cyclist.
Southwest (Neustadt (Weinstraße))
Mannheimer Straße near Hauptfriedhof. Place yourself at empty parking lots. Better accept direct rides to Neustadt because there is a bypass road around the villages and its hard to hitchhike further from there.