First off, you don't have an Inverter, it's a Converter. Get all the info on it you can & know how it works.
It sounds to me like the Converter is having some problems, but is obviously working or you wouldn't have anything.Inspect the 12 volt fuse panel & clean all the contacts. Check the output voltage also. When the battery is connected, there will be drains on the system, some normal & maybe some not. Install something like a Blue Seas battery disconnect switch to solve the issue while stored & not being used.
Another thing since you purchased it at auction, does the title read "salvage" or anything like that ?
I'm an expert in only one field....I believe it's somewhere in Kansas.
2000 / 22' SKYLINE NOMAD LITE
1998 DODGE DAKOTA / 5.2L= 8mpg.
2006 POLARIS ATV
1500/1200 Watt Champion generator
Yada Wireless Back Up Camera
1998 Dyna Wide Glide
USMC 68-74