Yes to both of those questions. I thought replacing those things might of fixed the problem. That is what I meant by both statements.
So, do I have this right? The exterior parking lights work when the separate Parking Lights switch is flipped to on, but when that switch is Off, the parking lights do not work when the headlight switch is turned to either the first or second "on" position, and in the latter case, even though the interior dashboard control lighting does work.
In that case, the most likely problem is the Parking Lights switch on top of the steering column. When it's Off, and the headlight switch is turned on, the power for the interior dashboard controls and the exterior parking lights comes from the tail & illumination relay. The power for the dashboard controls goes more or less directly to the control wiring, and because the controls light up, we know the relay works. But the power for the parking lights in this scenario goes through the "Parking Lights" switch on the steering column, even when it's Off!
The switch has two sets of contacts. On set is for when the ignition is off, and the Parking Lights switch is flipped to On to turn on the external parking lights. This we know works. The other set is closed when the switch is Off, and connects the power from the relay to the parking lights wiring harness. Because the parking lights wiring is good (because it's the same in all cases), and the relay works, about the only thing left is those "off" contacts in the Parking Lights switch. This has been seen before. Sometimes flipping the switch on and off repeatedly might restore the contact connections, but it's equally if not more likely the switch will have to be removed, and if the contacts cannot be exposed and refurbished, the switch will have to be replaced.
There's a small chance that the wire coming from the relay to the switch is bad. In one case the wire's connection to the switch had overheated, and the wire had separated from the switch, but that's an unusual situation.