Like you, I live way out, and I also have a big old tractor in a spooky old barn, so I can just imagine how scary that would have been!
I think I would have loaded the shotgun and fired it off into the ground a couple times as I walked out to the barn. Then I would have been ready with it as I checked out the tractor. If there was a person out in my barn, I'd make durn well sure that person was a lot more scared than I was.
I might say things like, "Get the night vision goggles, honey," and "Shouldn't we just set the dogs on him?" and even "Where'd you bury the last guy?"
Would I be terrified to go out there? Oh, yes. But that wouldn't keep me from making sure whatever turned on the lights was really a barn cat or an opossum or something. I'd be more scared to think someone might be CONTINUING TO LURK OUT THERE!!!
Aaaaaaaahhhhhh!!!!!!