Got a new battery. Battery light comes on then goes off. Lights cut off then on

What is your question?

95 Ford Crown Victoria. Battery light came on. Bought a new battery. After driving for awhile battery light cuts on and off. Radio, heater, and lights keep cuting on and off. When I step on the gas after sitting at a red light, the lights come back on then cut off. My car has not cut off yet. I also haven't had problems starting it yet sence the battery. Before the new battery when the car has been sitting for awhile I had to step on the gas so it wouldn't cut back off. Is this wiring, alternator, or something else?