On a delco alt conversion one time the gen idiot lamp was too small to excite the alt and I wanted to retain the factory original light so I added another bulb in parallel . Worked fine then. I would not suggest such a solution for your car but if you really had to have your LED light that might be one way.
They are about 7 other ways to excite your alt too providing your alt is not being excited by too small a current draw from LED.