The manual does not specifically warn against a permanent installation, but I saw at least four warnings or caution notes against leaving it connected when not in use (probably to avoid draining the vehicle battery.)
Notes:
1. Looks like you will need a circuit capable of delivering 100DCA to reliably power your inverter. Granted, surge current draw will not likely reach 83.3DCA, depending on the inverter's internal circuitry design. But that's a lot of power to supply to the inverter.
2. I believe the surge rating of your inverter is close to exceeding the Mirage's alternator capacity.
3. My calculations of a battery voltage of 12VDC is conservative. Most fully charged batteries will show a no-load voltage in excess of 13.5VDC, but when loaded the battery voltage is expected to drop some. It is my understanding that a device like an inverter can draw more current to supply it's loads when it's input voltage is sagging.
4. There are products made for trucking and camping that are designed to run on 12VDC. Consider some of those products instead of using inverters.
Google: 12V appliances There's some pretty cool stuff running on 12v.
5. Sorry for the long post! Good luck.