First make sure that the service brakes are adjusted properly Adjustment nut should be located either at the junction of the cables under the vehicle or at the handle itself (may have to remove trim for access) Pull handle to 3 clicks - wheels should be locked at that position
The 2003 Chevy S 10 emergency brake can be adjusted with the emergency brake adjustment bolt. The adjustment bolt will be on the emergency brake pad.
It he emergency brake has slack in it, then you more than likely the rear pads/shoes are worn out. Inspect the rear brakes.
You Tube "Happywrenching.com". Incredible video on how to change rear drum brakes on a 99-03 Protege. Did the entire brake job myself! :)
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Carefully drive in reverse while Spiking (agressively hitting) your brakes in intervals. Do this a few times and then drive forward, you should feel the difference in the amount of brake peddle you are now using. Repeat as necessary to fully adjust.
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Take apart the back brake and free the shoe or cable.
If it doesn't have the daylight sensor on the dash, you should be able to turn the DRLs off by applying the emergency brakes.