Your tachometer is equipped with a externally mounted shift light, make sure that the shift light cord is fully plugged in. Thet are usually shipped unplugged when new.
If your shift light turns on for 1 second when the power is applied, then it passed the bulb check. Next check you shift light set point per the instruction for your tachometer.
If the tachometer does not light for the 1 second bulb check, then access the shift light bulb and check the bulb filament. Your shift light has a replaceable bulb, if the bulb is bad, replace as needed. If the filament is good, check the power to the shift light with a standard automotive 12 volt test light. The two wires or contacts for the shift light will typically both show power until the light is commanded to turn on. One of those wires displaying power will turn into ground to illuminate the light when the trigger condition has been reached.