Go back to your last thread where I suggested a short in the Headlight Relay, and where the relay is likely to be found. Then come back with any questions on my explanation.
I'd also suggest you invest in a Bentley 240 manual, as it will be a big help with things like this. (You could probably buy one for what the new light switch cost.)

Here is how the switch works (from a Bentley diagram):

It's actually 2 switches that operate from the same shaft.
One works the Parking Lights, the other works the Headlight relay
They have different voltage inputs.
The PL sw. always has +12v (GN/R wire on input #30)
The HL relay sw. gets +12v (Y/Black wire on input X) when the Key is ON

In position 1, the PL sw. sends +12V out of #58 (Wht wire) to fuses 15 and 16 for the Parking lights. (The HL relay sw. is on a dead terminal at this time).

In position 2, the PL sw. goes to a dead terminal, and the Parking Lights will go out UNLESS...
...The key is ON. If so, the HL sw. sends +12v out of #56 (Y wire) to "pick" the HL relay.
The HL relay has the same +12v (GN/R) input as the PL sw, and has two (2) outputs when "picked".

HL relay output #87a (Wht wire) sends +12v to fuses 15 and 16 to keep PLs ON. (PL sw. now on a dead terminal, remember?)
HL relay ouput #87 (Y wire) sends +12v to step relay (on left fender rail) for the Headlights

The result is that the Parking lights (fuses 15 & 16) work from 2 sources — the switch in Position 1 and the HL relay in Position 2.
The Headlights work only from the relay, which works from Switch position 2 — IF the key is ON.

BUT—a short between HL relay 87a and 87 would let PL voltage feed back from fuses 15 & 16 to 87a and out from 87 in Switch Position 1. This relay can get real damp and cruddy, if it's where I said in the other thread. Especially after a few years. (Putting the car year in the subject header is a good idea.)

Hope this helps,

--
Bruce Young
'93 940-NA (current) — 240s (one V8) — 140s — 122s — since '63.