Hi,
Did the click happen on the inside of the vehicle? Was it under the dash on the driver's side? I'm asking because it is possible that the brake light switch is sticking and causing the brake pedal to not full release. What can happen as a result is the brakes are slightly applied. Over time, they heat up which causes the brake fluid to expand until the brakes are locked.
Okay, that is a theory at this point because this isn't a common issue. However, if it happens again, I need you to walk around the vehicle and see if there is excessive heat coming from the wheels and which ones seem overheated.
I have to be honest. There isn't a solenoid that applies the brakes. It is a hydraulic system. Something is likely dragging at times and causing one or move of the brakes to overheat. That's why I suggested checking for heat.
I don't know how comfortable you feel with working on the vehicle, but I am going to attach a few pics below that show the diagnostics related to brake drag. Note that it indicates the brake light switch among other things.
Take a look through this information and let me know what questions you have. I can't be sure, but I suspect the brake light switch is causing your problems. The sound you hear may be it unsticking. Let me know if when this has happened, if it was after driving a few miles.
Take care and let me know.
Joe
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Friday, December 11th, 2020 AT 8:41 PM