Brake light on after removing and replacing brake fluid

The brake pedal is firm and I feel no air in the system.

Given the recent service, it sounds like the float for the "low fluid" warning light sank and became stuck. On some models that float can be removed, and it's not unheard of for someone to forget to put it back in. It has a magnet built in that trips the switch when the float sinks low enough in the reservoir.

You can verify this by unplugging the "low fluid" switch. That should make the red warning light turn off.

Replacing brake fluid periodically is recommended by every manufacturer, but very few of us actually do this because that system is so trouble-free. I did this on my '93 Dodge Dynasty this summer. The old fluid isn't the problem. It's that brake fluid absorbs moisture from the humidity in the air. That can lead to corrosion of internal parts, but more commonly, it can lead to one form of brake fade by lowering the boiling point of the brake fluid from well over 400 degrees to closer to 212 degrees.

This drawing, step 6, is the closest I could find that shows the "Low Fluid Level" switch. If you can't read it, I can cut it into pieces and expand them for you, or you can copy and paste it into an MS Word typing program to make it bigger.

How can I remove the float on my car? And where is the low fluid switch at?

I just added to my previous reply. I can't find a photo that shows the switch, but there is a hole about halfway down on the side of the reservoir.

I just found this drawing that jogged my memory. If you have two wires coming out of the reservoir cap, those are for the "Low Fluid Level" switch. It's built into a plastic stick under the cap. The magnet is in a round plastic or styrofoam float with a hole in the middle the stick goes through. With that style, you can remove the cap, then run the float up and down by hand.

I should mention too about contaminating the new brake fluid. There must never be any hint of petroleum-based products in the brake fluid. That includes engine oil, power steering fluid, transmission fluid, axle grease, and penetrating oil. Most brake system specialists even wash their hands with soap and water before handling brake parts that will contact the fluid to avoid contaminating them with fingerprint grease.

We just added some related tutorials in this subject within the last week. You might want to take a look at these:

https://youtu.be/w7gUsj2us0U

https://youtu.be/nQRnKyVyMuQ

https://www.2carpros.com/articles/how-to-bleed-or-flush-a-car-brake-system