Have owned a Chassis W126 ('81 380SEL USA model) The 500 is virtually
identical. Consulting my old dealer W126 chassis manual(covers all
those chassis including SE & SD models, as well), I found a few items
that may help:

On the brake-fluid reservoir are two black-rubber buttons. Adjacent to
each button is an electrical connector. Under normal circumstances,
these buttons allow manual test of the low-fluid alarm. When either is
pressed, the red park-brake indicator should light. Press them. Perhaps
they are stuck. They should rebound to a convex-bubble shape. Perusing
the electrical schematic shows that the disconnection of those elec.
connectors adjacent to each button should disable this warning system,
making the light go off, and proving that the switch is stuck closed.

The parking brake switch is directly above the pedal-beam. Follow
upward from pedal, along the beam. Use a flashlight and prepare to
remove the velour cover underneath the steering column (medium
phillips-head screwdriver, and a little patience needed).
Check the status of that switch with Pbrake released.  Is it loose?  If
the metal beam is not pressing-in the switch, then the switch or
parking brakes may need adjustment.  The spec is no more than 4 notches
out of the 12. This is to say, when pushing the park pedal, it should
click no more than 3-4 times, before becoming solid to the feel.  All
Mercedes parking brakes are compIetely redundant to the driving brakes.
They are cable-operated drums, independent of the four wheel
disc-brakes. They only serve the rear wheels.  Which is great--you have
a *totally* separate stopping system available!  Unfortunately, the
park brake does not automaticaIly adjust, to my knowledge, as on other
cars.  It is a simple procedure, but very hard to describe.  Your
owner's manual may tell. I can e-mail the service manual pictures, if
you need them.
That parkbrake switch may be bad, or the connector to it. There would
be no harm in removing the connector and jumping the socket with a
piece of wire. This could eliminate or confirm trouble at the PB
switch/connector.
You didn't mention it, but it seems like the warning buzzer would sound
constantly.

A remote possibility is that the wiring from the instrument cluster to
the switches has chaffed, and contacted the grounded chassis metal.
This will *not* blow a fuse, nor pose a fire hazard.

Is it the "BRAKE" light or is it the round circle with dashes?

Pull up the parking brake pedel to see if light goes out... if so, then see
why your brake is not all the way up.

If it is the round circle... then you  need brake pad changed.