In the 99 Regal, the headlamp switch is also the dimmer switch for the instrument cluster.
With the headlights on, try rotating the switch to bring up the "nighttime" intensity.
If the headlight switch has a pre-set dimming function for the instrument cluster lighting (in other words, not adjustible by rotating the knob), then
replacement of the headlight switch would be the only way to fix the instrument cluster lighting problem.
See Wiring Schematic below.
Fig.1 - 99 Regal Headlamp switc & Instrument Cluster Lighting
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