Brake light not illuminating immediately when brake applied

From Fiat LOW Brake Fluid / Parking Brake Either the exclamation mark symbol or the 'BRAKE' dashboard symbol may be used on various models of the Fiat 500. Light should illuminate until engine has started. If light remains on, it signifies the parking / hand brake is on, or that there is insufficient brake fluid in the reservoir. If light illuminates and the handbrake is not applied, braking may become defective. Seek assistance from a Fiat technician immediately.

Check to make sure your parking/hand brake is fully released, sometimes the spring that pushes back on the mechanism isn't strong enough, doesn't push back all the way, and the brake indication switch isn't engaged.
The other possibilities are that the float in the master brake cylinder is stuck (if it has one), or the level sensor has failed.

According to the manual pg 10. http://www.fordservicecontent.com/Ford_Content/catalog/owner_guides/04expog3e.pdf
Anti-lock brake system: If the ABS light stays illuminated or
continues to flash, a malfunction has been detected, have the system
serviced immediately. Normal braking is still functional unless the brake warning light also is illuminated.

The exclamation light is an indicator that the transmission has a problem. Take it to a transmission place,for them to diagnose before it's too late.

This is not a good warning light as it relates to your Braking system !!!

Brake system warning light

This light will remain illuminated when the handbrake is engaged. Illumination after releasing the handbrake may indicate low brake fluid level (MUST CHECK THIS IMMEDIATELY AND RECTIFY).

Hope the information is useful ... be extremely careful and attend to this warning immediately if it is still on with your handbrake off and brake fluid top up!

this means there is a problem in the brake system of the car and u should seek service from a dealer or qualified brake shop. here is a copied section of your owners manual about the light.

Brake system warning
Momentarily illuminates when the
ignition is turned to the RUN
position to ensure the circuit is
functional. Also illuminates if the
parking brake is engaged. If the
brake warning lamp does not illuminate at these times, or remains on
after releasing the parking brake, seek service immediately.
One of the following conditions may exist:
² low brake fluid level in the reservoir.
² Brake force distribution system failure. The ABS light will also
illuminate if this condition is present.

According to the 2003 Ford TaurusOwners Manual:

"Brake system warning light: To confirm the brake system warning light is functional, it will
momentarily illuminate when the ignition is turned to the ON position when the engine is not running, or in a position between ON and START,
or by applying the parking brake when the ignition is turned to the ON position. If the brake system warning light does not illuminate at this
time, seek service immediately from your dealership. Illumination after releasing the parking brake indicates low brake fluid level and the brake
system should be inspected immediately by your servicing dealership."

In short, as your brake linings (pads and shoes) wear out, the brake fluid level in the reservoir goes down.

You're probably right at the point where the level gets low enough to turn on the warning only under specific circumstances (cornering? hard braking?).

You can top off the fluid for the short term, but you should have your brakes inspected fairly soon.

just a little bit low on brake fluid

check all ground points of harness and @ tail light

Sounds like your brake light switch is on its way out. Its a simple fix and a cheap part. It will need to be done immediately as not only can the lights staying on drain your battery but it can also cause lack of power and not put the brake lights on when braking. The switch is operated by the pedal itself and requires the drivers underdash trim to be removed. With this off the switch can be accessed and replaced. If you can get a vehicle technician to fit it, do so, as they are quite fragile and new switches can become useless if fitted incorrectly. Good luck

I have the same problem with my 2004 Trailblazer LT. Driver side brake light does not illuminate. All other lights work fine. Replaced bulbs. Still does not illuminate. Cannot figure out which fuse goes to this light. Could it be a fuse?