I don't log into Moparts as much as I have in years past, so it's been a long while since I looked over any of this Road Lamp stuff. Please take the following info with a grain of salt, but hopefully it will help you figure out what's going on.
I do remember that road lamp relays regularly cause confusion.

If I remember correctly, the main issue was that people expect the relay to turn the road lamps on, when actually it's purpose was to turn the road lamps off when the high beams came on.

If your road lamps come on when you unplug the relay, then maybe your highbeams are on?

Most of the following info was saved from a previous Moparts thread over a decade ago. That's where the 70 harness pic screamindriver posted came from...

L34 Road Lamps

The cuda road lamp moutning brackets and the Switch and relay are different between 70' and 71'

In 1970 the relay controls parking and side marker lights as well as the lights on reminder buzzer, 1971 controls the above plus the road lamps.

If I read that diagram right the relay has nothing to do with the buzzer. The buzzer is attatched to the switch. Correct, however the relay is not a stand alone circuit, nothing in the circuit works without the Road Lamp Switch.

The relay applies power to the lights and they are turned off by the relay when the highbeams are on. - The Road Lamp Switch applies power to the relay which applies power to the lamps. The foot dimmer switch will turn off the roadlamps if the high beams are turned on.

If the lights/switch is left on the buzzer buzzes same as the headlights. Right/Wrong? If the Road Lamp Switch is left on it will trigger the buzzer, the headlamp on buzzer is triggered by the parking/side marker lights that are turned on when either the headlight or Road Lamp Switch are turned on.

In 1970 the switch turned on the roadlamps directly.

70 relay does only have 3 terminals 71 relay has 4 terminals plus the extra wiring/connectors going down to the dimmer switch

1970 relay circuit have the following leads.

L20 and L20A - Lamp out and power direct from the switch.
L6 and L6A - Park and side marker lamps and Headlight buzzer diode
L21 - N/A
M5A - Power
Q13 - Headlight buzzer diode

relay part #s '70 - 3004186
'71 - 3513557

Key and headlight buzzer the same in '70

Are 70 road lamp brackets the same as 71?
No, they are not the same. 1970 versions are a two piece bracket (two parts welded together). 1971 style is the same basic shape but a single piece stamping. BTW, original 71's are really hard to find!
How do I figure out if its an original road lamp bracket Any P/N or Pentastars to look out for?
1970 roadlamp(two piece welded together)brackets had an "R" or "L", but 1971 (one piece)brackets had "RH" or "LH" for left or right hand. that's it, no other numbers. There are some reproductions that have them as well. The key to ID'ing the reproductions is that they were not stamped as originals, they were laser or water cut and have serrated edges accordingly rather than the pinched through-sheared look of a stamped parts edge.