The symptoms you describe are usually caused by an alternator fault. The warning lights are wired in such a way that they all illuminate until the engine starts and the alternator generates an output. This gives a warning lamp test at each start. Loss of alternator output will illuminate all lamps, not just the battery warning.
107.023: 350SLC, 3-speed auto, icon gold, parchment MBtex (sold 2012 after 29 years ownership).
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201.028: 190E 2.3, 4-speed auto, blue-black, grey MBtex.
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