You're logic sounds OK and these are simple electrical circuits - one for each of the brakes which activate the same, single brake light.
So, either the back brake or the front brake circuit is continuously live; that indicates that one or the other has a fault in the switch that operates the brake light. Suggest you check them - for instance the back brake light is operated via a simple spring which if too tight will keep the brake light on, even if you are not pressing the brake pedal.
If you say what model of bike it is then others may have more detailed information.
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Dave
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