Hi, I also have a 2002 TJ. I have replaced all my lights with LEDs. Yes, a new flasher should fix your fast blinkers, but I unfortunately don’t remember where I bought mine. I thought it was Amazon, but I don’t have the order history. Sorry.

Another issue you will run into is the electrical design of the side marker lights is a 2 wire system, using a floating ground. That works fine with an incandescent, but not leds as a led allows current to only flow in one direction. I installed a conversion kit called the blinker genie 2, and it was worth it in my opinion. You’ll need to add a ground wire to each marker light for this kit.

Link to blinker genie: https://www.amazon.com/dp/B07DQRPRLW/