Call DESPP records department and get the date they sent the background check back to the PD. Make sure you have your money order receipts handy when doing this so you can provide the money order numbers/information so they can track it, this information typically is required due to the confidentiality of everything and serves as proof you are who you say you are, and helps locate the proper information. The phone number to call is: 860-685-8480 AND ASK FOR 'RECORDS'. Sometimes they'll give you the runaround too. if this happens, just keep calling every half hour or so trying to maintain politeness haha, until you get your answer.
then you can call the PD again to inquire on the status of your permit. if they tell you they're still waiting for your background check to come back, you can immediately tell them you know exactly when they already received it and tell them the date according to DESPP. they'll probably be at a loss of words, or come up with another excuse, and you can go from there however you see fit, possibly mentioning an appeal if you so desire.
Chances are though, you'll probably need to appeal. Know though that by filing an appeal, you typically don't need to wait to actually have the appeal hearing. the BFPE will send info to the PD and whatnot, and that usually kicks em in the rear to get your application finalized, typically resulting in the permit being issued fairly quickly. typically, not always.
from what I've gathered, Seymour is horrible about pistol permits, and without an appeal they often can take several EXTRA MONTHS to issue a determination, at which point you can no longer appeal because appeals need to be within 90 days of the timeframe used for the reason for appeal