Stir mustard and salt in a medium saucepan. Gradually stir in enough vinegar with wire whisk or fork to make a smooth paste. Stir in remaining vinegar, corn syrup, brown sugar and caraway seed. Add eggs one at a time, whisking until blended.
Cook over medium heat, stirring constantly, until mixture thickens, about 5 to 10 minutes. Do not boil.
Pour into 1/2-pint jars (or other containers with a tight fitting lid); cover.
Refrigerate at least 24 hours before serving.