The Corvette has a pretty complicated electrical system in the dash. I have a 1990 and have extensively studied the wiring diagrams from the original GM Factory Service Manual. ( I must say that GM has an outstanding manual, especially in the electrical areas).. Neither Chilton nor Haynes manuals will even come close. They are much too general and don't cover the necessary details.
The C4 has an analog interior lighting controller with the adjuster lever located behind the headlight knob. That feeds a signal to an analog regulator amplifier which looks like a large shinny heatsink located below the steering column. That analog regulator source feeds ALL the interior lights and control backlights everywhere. However there is also a digital PWM (pulse width modulator) that is triggered from that control system, that is located inside the central body control module (located deep behind the radio). That CCM supplies ALL the "illumination voltage" to everything in the Instrument Cluster, AC Controller, and original Radio (but not the actual tach circuitry itself). The PWM from the C4 CCM is usually very stable, but I have seen situations that cause the PWM to be unstable and cause the instrument panel light to flicker. This can usually be heard as an unusual noise on the AM radio band. The noise will be in sync with the flicker. This seems to be always cause by an intermittent ground connection, of which there are several. This is where the OEM factory manual really shines. It shows you in detail where every ground connection is made and what connectors are involved and where they are all located.
On my own C4, I had lots of problems with moisture corrosion on the back of the instrument cluster that caused all kinds of no-light problems. I disassembled the cluster, cleaned all the circuit board and connections, and replaced EVERY light with LED lamps I got from
www.SuperBrightLEDs,com . I tried using the 161 socket adapters they sold to mount these new LED lamps, but still has some loose connections, they didn't fit the GM circuit board correctly. So I finally discarded the sockets and soldered the new LED lamps to the circuit board directly. (I thought that LEDS should never fail and they will never need replacing again). It came out beautiful and the LEDS are about 50% brighter than the stock 161 incandescent bulbs. I now have no flicker of any kind and outstanding illumination everywhere. I have since proceeded to replace a lot of other bulbs with LED replacements too.
As for the unstable tach, again I recommend checking for a poor ground. The tach circuit is very simple and all on the PC board in the cluster. There is no special filter shown but there is a white ceramic calibration resistor chip (examine that for a rare crack in the black carbon). All of the gauges including the tach share a common ground wire circuit and "connection pin" on the back of the cluster and this connection is not common to any of the lights. My pins were corroded. Watch the battery voltage gauge. This is connected to the same gauge circuit and will flicker if that voltage is not constant. If the voltage gauge flickers this is a clear indication of a faulty ground.
Good Luck
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