Vinegar is a very poor electricity conductor because it lacks free ions. Electricity is created when ions are available within a solution to carry an electrical charge.
Distilled water conducts no electricity because the ions have been removed from the water. The addition of salt to the water increases the sodium ions in the water, which conduct electricity well. Both vinegar and ammonia have very few ions to carry an electrical charge, so very little electricity is conducted. However, when mixed together, the two liquids react with each other releasing ions, and the resulting solution becomes a very good electrical conductor.