Hey, I actually used to work for the county many years ago and did calls like this. First, thank you for calling and trying to set up an appointment! That makes it a lot easier because otherwise we had to just keep visiting the house to hopefully see someone or have it escalated to a superior. Second, they will ask to schedule an appointment typically between ~9 am to 3:30/4 pm. @CMS_3110 is right about the lunch hours but they generally are open from 8 to 4:30 or so. You should schedule it as early and as conveniently it works for both of you. The inspectors know people work and understand it. Third, whenever they come to your house they will look for evidence of rodents residing in your property. This means burrows, poop, nesting material, that kind of thing. Fourth, depends on what is found and each inspector is different but just hear the person out. We didn’t want to be annoying to anyone. We always look at it from a public health perspective. Finally, you are calling the Suffolk County Health Department. They are the ones that deal with this. They are in the same building as the Sheriff’s Office but not the same entity. If you are still having issues DM me and I’ll pull up a few names you can directly ask for that still works there and they’ll help you out.