88 Ford Taurus battery discharging

88 Ford Taurus, 3.0L V-6, when I turn off the engine the brake light (on the dash) barely illuminates. I also hear a noise which I traced to the injectors. I can feel them vibrating. But if I put the parking brake on the
light goes out and the noise stops. If I don't put on the parking brake the battery will go dead overnight. A code reader I bought doesn't show anything. I also took the car to two different auto mechanics, but the problem is intermittent and did not duplicate for them. I have checked all ground points I can find, but all are tight and not corroded. Any suggestions?

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