Never ending story. My wife is making fun of my car because there is always something wrong with it. Now that is the parking lights I can't turn off after shutting down the engine and removing they key, with the light switch pushed all the way in. The two green arrows on the dash (left and right) stay on as well. Even when I drive. I believe that is the switch itself I need to replace. Any advice?  

The turn sig indicators staying on suggests a short to power somewhere. Not likely in the headlight switch tho....but anything is possible. The headlight switch always has battery voltage, even with the key off, so that might be the place to start. Unplug it and see what happens. You could put a new switch in and still have the same problem tho, and if so, then the real problem is most likely in the turn signal switch, or possibly the hazard warning light circuit/flasher. Lectrical issues on these old gals can be frustrating, to say the least.

That was my fear when I asked my question on the forum. I kind of wished this was coming from the switch, but I can't see why the two turn signal indicators would be involved if it was the case. I should be prepare to sweat a little...

OK. Indeed, the switch seems to work fine. I unplugged the turn signal flasher (on the passenger side). No change.

I then went to the hazard flasher (on the fuse box) and unplugged it: Everything went off.  I thought that was the culprit. I bought myself two new flashers and replaced them both.

Turning signal works fine, both sides.

Last thing I am missing are the back up lights. The car is parked with the reverse engaged (anti-theft feature). With the key in and turned on, shouldn't I get the back up lights on even if the engine does not run?

I gotta ask....are you sure the hazard switch isn't ON?

Yes, Adam, spot on! I found your question after I found out myself, but it took me some time. Embarrassing.

Still, I am still in trouble. No parking light, no instrument light, no side marker, not even back up light. Fuses look OK and turning signal works, as well as headlights. Driving me crazy.

OK. Now I the turning signals work, - both sides - when the light switch is pushed all the way (lights off).

However, when I turn the lights on, the parking lights light up as well as the instrument panel, including the two green arrows (turning signal indicators) and the turning signal does not work anymore (no flashing).

Can't get why.