Do you have a light bulb in the garage? Use it to add a plug. Seen this many times at self storage place where the units dont have wall sockets but do have lights, so people tap the lights for power.
https://www.amazon.com/Light-Bulb-E2...a-610647614338
By the way, please pay attention to wattage. That power inverter is only rated for 300 watts while the heat gun is 1500+ watts. That inverter will never run a heat gun.
a 2000 watt inverter will cost $300+ and run your battery down in 30 minutes.
For a super high power draw device like a heat gun, battery and inverter is a bad choice.