Engine overheat, low oil pressure, or alternator voltage.
Could be something like low fuel, high temp, low oil pressure, any number of things.
The alarm is set, activated, or malfunctioning.
There is no reset for a check gauges light. If the light is on, there is a problem either with the temperature oil pressure or voltage.
Bulb is probably defective. Replace it.
Guessing bad headlamp switch. No power to taillight fuse feeds dash fuse also. Need to glance at wiring diagram to troubleshoot fast.
One of the gauges is outside the safe range. Check oil pressure, coolant temp, and battery voltage.
See related question below.
It is inside the transmission on the valve body. It is called a transmission range sensor.
When one of your gauges shows something abnormal, your "check gauges" light will come one. Chances are you're low on motor oil. When you corner, the oil will slosh away from the pickup, causing your oil pressure gauge to read zero for a second. This in turn causes your check gauges light to come on, but by the time you look at your gauges, the oil has settled in the pan is your oil pressure is reading normal again. When you see the check gauges light and the gauges are reading fine, check your oil.
The check gauges light means that one of the gauges is out of the safe range.
It could, you need to have the codes checked to know possible causes.
Your 89 New Yorker has a peice of trim at the bottom the tail light, in that small piece of trim is a screw. Take that screw out and you can get to the rest of the screws that hold the tail light assembly in place, Oh yes most important you must have the trunk lid raised so you can get to the wiring harness.