Unless playing with the switch has a direct result in curing the problem, it could be more involved.
The parking/panel illumination lighting isn't hardwired to the headlight switch, but controlled by the BCM (body control module) and FCM (front control module) over the PCI (programmable communication interface) communication bus that carries messages between the modules.
The headlight switch sends a ~0.5v to 4.5v signal to the BCM depending what mode is selected. (If the headlight switch was ever unplugged and the BCM saw 0 volts on the lighting signal line, it would then turn the headlights on as a safety default).
The BCM then interprets what mode the driver selected and sends a command over the PCI bus to the instrument cluster for panel lights and how bright they should be.
It also sends a command over the bus to the FCM which is part of the IPM (integrated power module-the underhood fuse/relay box) to energize the parking light relay (that you will find inside the IPM) along with left and right side parking lamp fuses. Do the headlamps operate OK?
The only lights on the vehicle that are 'directly' controlled by a switch are the hazard lights and brake lights.
You might try swapping the parking light relay with a similar non-critical relay nearby. Corrosion can occur at the FCM terminal pins where they plug into the front of the IPM and underneath the IPM where the harness connectors plug in due to road and battery acid spray. The BCM usually stays nice and dry inside the vehicle. It can do intermittent things, but is fairly reliable.
The FCM and BCM can store fault codes and run tests that might help diagnose this, but would need an advanced scan tool (like the DRB III or equivalent), to do so. These diagram links below may differ slightly in wire color, etc., but are similar to the general layout found in your own vehicle.
A factory service manual with wiring diagrams and a voltmeter may be your best friend tor finding the culprit. It would probably have to act up for you in order to prove the faulty component. This is the stuff that makes 'intermittents' a challenge sometimes.
Parking lights:
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Instrument cluster illumination lights:
Plymouth+Breeze+2000+Dash+Light+Wiring+Diagram.jpg