Running lights are on ??

So this is where the relay was hooked to. Headlamp buzzer. Wire harness matches and wire Color’s match . It’s currently feeding power to the running lights with the key on. (Assuming the relay buzzer thing is bad). With the key off the headlight switch only feed the two headlight . I tested the wires out of the headlight switch and none have power in running light mode.tried three switches
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You misunderstood what I said. All Mopar switches in these A bodies work like so:

(First, unrelated, the headlights ONLY has a separate batteyr feed comes UNfused from the ammeter circuit)

The second switch section is the tail/ park, you have TWO output terminals. When you pull the switch to "park" BOTH tail and park terminals are live

On later cars to get the full time running lamps, all Ma did was to move the park wire over to the tail terminal. The tail terminal is live EITHER in park or headlamps, so with the park lamps wired in parallel to tail, they all stay on either park or headlights.