That red BRAKE light it shared by the two systems - one being the Service Brakes - those Hydraulic ones, and then there's the HANDBRAKE - the one with the Handle you pull - also called Parking Brake.
When the Parking brake handle is lifted - it will set an alarm after about 3 seconds of it being on - to notify you - then check your console for an alert message - that might help you narrow down where this fault is.
Have you checked the Brake fluid container recently? IF you have not done so, might want to grab a flashlight and shine the light thru the container - that white plastic, and see if you can even see a fluid in there.
The thing is a clam-shell - and is not the larger coolant tank - its the one over where the Brake system is - and uses a cover that tells you what it is and what you use to fill it. Where the clam-shells will meet - that flange - is where the top of the fluid level should be.
If that is OK, then the Handbrake system needs a little TLC and if you're not comfortable with tearing apart your interior to get at the Handbrake ratchet mechanism - then set up an appointment to have you Brakes inspected.
Else double check that you're not lifting the handle or the handle itself has something jammed in the knockout hole it uses to cover the mechanism - keeping the handle lifted and able to trigger that BRAKE indicator on the dash at key times.