I'm wondering if someone had tampered with the wiring behind the indicators at some point and miswired something.

It seems like the brake pad wear indicator would illuminate in that manner, unlike the battery indicator, which would just come on solidly, no matter what driving characteristic may occur.

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2009 ML350 (106K) - Family vehicle
2001 CLK430 Cabriolet (80K) - Wife's car
2005 BMW 645CI (138K) - My daily driver
2016 Mustang (32K) - Daughter's car