it is not until i remove the spade connector with the two white wires attached to one connector, that the lights turn on and off like they should.

If those are the white wires feeding fuses 15 and 16, you really have me stumped. Let me ramble a little, on the off chance I say something sensible...

1) With the Key off, the only places that should have +12V are the inputs to the Parking Light switch and the Headlight main relay.

2) There should be no +12V on those wires at the fuse input. They normally get +12V (to feed parking and tail lights) from two sources:
a) From the light switch (only in Parking position)
b) From the light switch in Headlight position ("a" goes away when switch is turned to HL position)

3) An erroneous +12 on those white wires(regardless of source) could also power the Headlights, but only if the Headlight relay is the wrong type (outputs 87 (HL) and 87a (PL) are always common).
But that would mean always getting Headlights with Parking lights, even with no other fault. Some might not notice that, if they never use Parking lights alone.

4) I just can't see the relay at fault here. I've seen bad ones (burnt, shorted terminals, etc.) but can't imagine any bogus relay condition that would be "corrected" by pulling those white fuse wires.

5) Right now, I'm ashamed to admit to seeing no single fault anywhere that would give that kind of "power" to those white fuse input wires — or allow the lights to "turn on and off like they should" if those two wires are disconnected from the fuse input terminal.
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Bruce Young
'93 940-NA (current), 240s (one V8), 140s, 122s, since '63.