Why not build LEDs directly into the cartridge? For DJ's or home use, I suspect that the most popular light right now is by Ikea.
The only other cartridge with LED that I could find is from DS Audio https://www.whathifi.com/news/worlds-first-optical-phono-cartridge-to-go-sale-ps6250 but they are in the business of mechanical->optical->analog conversion
So yeah, go build it yourself, but if you do it commercially without me, you will be named and shamed :D Haha, might open a mod shop
LEDs were saved form my old Nokia 3100 that were used to light up the keyboard, only measuring around 1.8x0.65mm super tiny and lightweight