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I had that issue with my 2004 Mountaineer. In fact, when I purchased it, the car salesman mentioned that the speaker had been replaced. I said that was interesting since it didn't work.
I've read a TSB related to water getting in the connectors and corroding the terminals. That may have been the issue with the passenger side. When the radio was turned up, the speaker usually would start to work. I could then turn the volume down and it would continue to work for awhile.
However, later the driver's side speaker stopped working. That was due to a broken wire in the rubber boot between the door and the cabin. So when I re-wired the driver's side speaker, I also ran a new wire for the passenger side. While I had everything apart, I installed a set of 4-way Kenwood speakers and haven't had any issues since. Running a new speaker wire for the passenger side was a piece of cake compared with the driver's side.
Sounds very possible. Fortunately the door panels remove easily! For the door ajar light I'd be more inclined to suspect a dirty switch rather than a wiring issue.