That warning light also works off the brake fluid level. There's a plug on the lid of the reservoir in the engine bay, this detects the level. When you brake heavy, or go downhill, the fluid moves away from the sensor and will be "low" to the sensor.
Park on a level surface and check the brake fluid level. Top it up.
It also works off a switch located just under the handbrake lever, so when driving, just lift your handbrake ever so slightly to see how sensitive it is. But it sounds like your fluid level is low to me.
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