I would install a battery back up for the door/alarm system any way.
Its very simple and cheep to do:
You install a very small 12volt battery " one for emergency lighting because they are all 12 volt and gel cell" then solder a diode between it and the power supply from the truck. the truck can replenish the battery but it will not drain when the batt in the truck goes dead. Ta da problem fixed.
You can always get in your truck even if it does not start.
Most of my expensive cars have these and i installed all of them my self.