Can a bad rear tail light blinker bulb cause the Check Charging System light?

What is your question?

Rear tail light blinker bulb goes bad occasionally. Can tell from quick blink on dash when engaging. Last time this occurred I dallied in changing the bulb and at a stop light the check charging system light came on, headlights dimmed, etc. Barely made it home. Battery had 10.5 volts on it, so I charged it up; replaced bulb and everything seems fine. Had auto zone check charging system and everything checked out okay. Anyone have a similar situation?

What makes this problem better or worse?

first time this happened

How long has your 2003 Ford Explorer had this problem?

A few days