So after YEARS of attempting to figure out the issue, I believe I have isolated the problem. Let me say that I tried every single thing an internet search (and forum suggestions) yielded. So all the things like calibration, gas cap, brake booster, electrical lines, sensors, brake light switch, etc. - ALL of it was looked at or replaced and nothing helped.

About a month ago I swapped out my rear brakes and decided to remove the ABS sensors on the bearing assembly (simple one-bolt, pull out removal). They were caked in bearing grease. The REAR wheel bearings are no good. The grease that's been flinging from them internally covered up the rear sensors and caused the issue. I cleaned them, put them back, and the lights now function perfectly as they should. I have since replaced the driver side wheel bearing / axle, and have plans to do the passenger side next when finances allow.

For anyone who has struggled with this issue as long as I have, this may be your solution. Check your rear wheel sensors to ensure they are clean. Hope it helps someone out there in the future.

Same lights were on for me, but it was my rear wheel speed sensor/abs wire harness. For any future readers of this thread, a gas cap will NOT cause ABS lights without check engine light!

For OP, if your lights do come back, I suggest you get a code reader that is capable of reading ABS codes and it will point you in the right direction.