I too, upstate, the county I'm in has just like you say electrical on general building permit but also has an electrical permit for if the electrical is not part of a larger build.Third party inspection is required for either permit. All electrical in most of the townships in the counties I'm in are asking for a permit, although some of the "hacks" (handy man and untrained wannabes) around here won't even bother, just do it and hope they dont get caught. Any larger job I will get the third party inspection even if the local township doesn't require permit, one more level of safety and my insurance requires it, as it "gets them" and me "off the hook", as it were, the third party inspections will take some of the liability in event of catastrophic failure. If there is a failure they will also check if 1. Was a permit pulled, 2. Was it inspected. They will always look to "who was the last to touch it" for blame, and getting the above helps in defences. Not speaking from any direct experience, just from others I have known to get bit.
We live in the "wild west" of electrical service and maintenance here, where anyone can put up a shingle and do electrical work, an LLC or license makes no difference to "staying within my county" here. Make sure you get your insurances, you don't want to be doing this sort of work without coverage, life and property is at stake and it can come back to bite you if there is a failure, even with and LLC. Also make sure you get educated and stay updated and stay up to date with the code, technology is always wchanging, and that will show as you meet with inspectors to check your work, they will notice.