The brake switch that controls the brake lights is under the dash. The pedal rests on it when in the up position. Could be that the switch isn't releasing when you press the pedal.
^^^I was going to suggest that as well...i had a issue 2 weeks ago where the pin that makes the lights turn off once the pedal is released was rotten...but yea, that could be his problem.
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Did you replace your bulbs with same type? Brake lights have bulbs with 2 wires in bulb and the bulb has 3 connecting points. But first check if the new bulbs are working.
BTW, is the brake light indicator always on?
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