What do you call the red light near the tabernacle?

I believe you are speaking of the "red light" in Roman Catholic churches. The "red light" is called the "sanctuary light." Its purpose is to let people know if the "Blessed Sacrament," that is, communion bread and/or wine, that has been consecrated during the Mass, and is believed by Roman Catholics to be the Body and Blood of Christ, is actually present inside the Tabernacle. If the light is on, the "Blessed Sacrament" is present inside the Tabernacle; if the light is off, the "Blessed Sacrament" is not present inside the Tabernacle.