Try this. Observe the dashlight brightness with the engine running at at fast idle and your headlight switch only out one click. That is parking lights only along with dash lights. Then pull the switch out the rest of the way to make the headlights come on. If the dash lights go dimmer then the relay will correct your problem. If the dash light brightness is unchanged, you may have a problem elsewhere such as a weak battery or a defective alternator or voltage regulator. Voltage at the battery with the engine at fast idle and all accessories off should be around 13.6 or 13.7. If it will not acheive at least 13 volts something is wrong and that will cause all lights to be dim with the dash lights being the most perceptible.