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I would just pull the fuse for the remote starter instead of removing it. I have no idea why it started... maybe some type of radio interference glitch type of thing?

 

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Does this happen at around the same time of the day? Some of these units are fairly sophisticated and maybe it can be programmed to start on a schedule. I know you don't use the remote starter but maybe something (low battery, electrical issue) has triggered something like that.

You might also keep an eye on neighbors to see if someone is starting their vehicle at the same time.