Coincidentally, I've just run in to this very same problem. Think MRRSM has got you pointed in the right direction with a wheel speed sensor. Here are my symptoms. Might help you diagnose. I don't have this completely solved yet. Not trying to hijack this thread, but I'm battling the same exact thing.
Left front brake has been "grinding" when engaged on rare occasions for several years. Changed pads, rotors, and fluid about a month ago. Still getting the occasional grinding. I came to the conclusion that its the ABS engaging on that wheel.
Wife started complaining about a week ago that the ABS light was coming on occasionally (the TB is her DD). It would not stay on - just on and off randomly (seemingly). Decided it was time to clean the left front speed sensor per the video above.
Took everything apart yesterday morning. I have Timken hubs on my truck. They put a small stainless steel tab under the speed sensor mount, presumably to combat the lifting issue from corrosion. When I pulled the speed sensor, I could see purple grease in the cavity where the toothed sprocket is located. Many of the teeth were bridged with grease. I had a spare Timken hub (not new, but not failed either). Decided to take the speed sensor off the spare and install it.
Well, changing the speed sensor made things a lot worse. ABS light was on constantly AND random brake light with chimes - almost non-stop- just as the OP describes. You can get the exact behavior described by the OP due to a speed sensor.
At that point, I decided to change the hub. Figured it was close to failure anyway with the purple grease in the sprocket cavity. It was about five years old with about 80,000 mi. Didn't want to put the used Timken on. Had to buy a Moog from Autozone. Killed me to pay $180 when I could have got a Timken from Amazon for $125, but I wanted to get this done.
After installing the new hub, ABS light is still going on and off, but the brake light and chimes have stopped. ABS light will shut off for a couple of miles and then come back on for a few miles. Essentially, I'm back to square one. Starting to think I'm barking up the wrong tree with the left front speed sensor. I have the Torque app which, as was already mentioned here, won't read ABS codes. Was seriously starting to think about taking it to the stealership to read the ABS code rather than keep guessing. Decided not to give up so easy. This truck has not seen the inside of a stealership or any other repair facility in over 11 years due to help from this site and OS before that. Decided to buy the BlueDriver bluetooth transmitter for $100 to use with their app. Claims to read ABS codes. Figured it would cost me about that much to have the stealership read the codes anyway.
BlueDriver thing will be here tomorrow. I'll let everyone know what it says.