I would pull a wheel and take a look.
After your brake light first comes on, you have plenty of time to line up parts, tools, etc. If I understand correctly, the light will eventually go out and this does not mean your brakes are suddenly healed but that the sensor is now totally gone.
I was a complete novice when I did my front rotors and brakes. A very simple but dirty job that you can do for about $150. Anywhere else, it will be $500+.