I don’t think you would have burned up the brushes with a short circuit like that. To test the voltage with a voltmeter just run across the battery terminals when off. Record voltage. Start the car and record voltage. When running <12 indicates that the alternator is charging and that is not the problem. IF the voltage is too great of a denomination (<14) your voltage regulator is shot. Id check the wiring of the lamp to make sure that is not shorting out causing a voltage drain that is just running your battery dead. Good luck

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1983 Mercedes 300SD
1987 Mercedes 300SDL
2001 VW Passat 2.8 AWD
2007 OM642 Jeep WK 4x4