The Parking Brake could be set (even slightly)
No but, the brake fluid level will drop as brake pads/linings wear.
The brake light in your dash will turn on if the brake fluid level is low in your brake master cylinder in your engine compartment
Is the brake fluid level low in your brake master cylinder in the engine compartment ?
check fluid level
In a 2002 Ford Explorer Sport : You check the brake fluid LEVEL in the brake fluid reservoir in the engine compartment . It is on the drivers side of the vehicle , near the firewall ( that's the metal wall that divides the engine compartment from the passenger compartment ) It is a plastic reservoir that allows you to check the brake fluid level just by looking ( you only need to remove the cap if the brake fluid level is not up to the full mark and you are going to add the DOT 3 brake fluid that is required
If the brake fluid level is low you really need to have the brakes inspected for your own safety.
It could just be that when you push the brakes the fluid level goes below the proper level. add fluid and see if stops.
To compensate for the wear on the brakes. As the brake pads wear down, they move closer to the rotors, and this brings the brake fluid level down slightly. Note: it is not a good idea to continually refill the brake fluid reservoir because a mechanic needs to check the level for an estimate of how much the brakes have worn. If the reservoir is full all the time it would appear that the brakes are not wearing down (which we know isn't true).
Check the level of brake fluid in the master cylinder reservoir. If it is low that will illuminate the brake light also. If it is low on brake fluid it's time to have the brakes serviced.
Check the brake fluid level, it is probably low. If so, this is an indication that your brakes are in need of replacement.
bleed the brakes. check fluid level
Check the brake fluid level in the reservoir there is a sensor there that will make the light come on if your level is low.