I kind of went down a rabbit hole from your other post about this and the link in this post. I looked on-line about flickering LEDs and found too much information. The fact that your turn signals work with the engine off, and then flash faster with the engine on would lead me to think the engine is effecting the flasher module. I know you can get a noise suppressor to keep engine noise out of the radio, why not put one on the supply to the flasher module. It's usually either a coil in-line, or a capacitor to ground. I found some with both. Here is a link to a site with a nice picture, you could probably get one at your FLAPS:
https://radiogagas.com/product/25a-a...utm_term=33517