ETC light flashes and only goes away after restarting the vehicle after changing the engine oil cooler?

A flashing ETC (Electronic Throttle Control) light usually indicates a serious throttle system issue that could cause reduced power or limp mode. I would service the throttle bore and then run the codes and clear them once the service is done.

https://www.2carpros.com/articles/throttle-actuator-service

This guide will show you how to run the codes and then clear them. Here is how to do the service for your car.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Check out the images (below). Please let us know what happens.