There can be several reasons why your battery light is on but goes off when you accelerate, even after installing a used newer battery. Here are some possible explanations based on the search results:

1. Loose wire: It is possible that there is a loose connection between the battery and the alternator. Check the wires connected to the battery and alternator to ensure they are properly connected [3].

2. Slipping belt: A slipping belt, also known as a serpentine belt, can cause the battery light to flicker when accelerating. If the belt is worn out or deteriorated, it may slip under a heavy load, causing the alternator to lose grip and free-wheel. This can result in a drop in power and trigger the battery light [3].

3. Faulty belt tensioner/pulley: A faulty belt tensioner or pulley can wear out the belt quickly and affect the performance of your car. Inspect the tensioner and pulley for any signs of damage or misalignment. If the tensioner is oscillating, making squeaking or rattling noises, it may be causing a loss of voltage when accelerating [3].

4. Failing alternator: The alternator is responsible for generating electricity to recharge the battery and supply power to electrical components. If the alternator is failing, it may not be able to supply enough electrical energy, especially under heavy load. This can result in a drop in power and trigger the battery light. Signs of a failing alternator include inconsistent brightness of lights, non-functioning or slower operation of accessories, a dead battery, and strange noises or smells coming from under the hood [3].

5. Failing voltage regulator: The voltage regulator is responsible for maintaining a consistent flow of electricity to various car components. If the voltage regulator starts to fail, it may not be able to keep up with the car's demand for electricity when accelerating. This can result in a drop in power and trigger the battery light. Signs of a failing voltage regulator include inconsistent engine performance, intermittent acceleration, and engine stalling [3].

Learn more:

1. Blink Fast! Why Your Car Battery Light Comes On and Off
2. Battery light comes on during hard acceleration - Maintenance/Repairs - Car Talk Community
3. Reasons why your battery light comes on when accelerating - Mechanic Ask