This town-court.com website has a feature where users can post comments about courts. The most common type are complaints that the courts don't answer their phones or that the staff are unhelpful. Two good examples are Philadelphia Traffic Court and Jersey City Municipal Court. There are at least three reasons why courts are bad with phone calls.
First, courts don't have the customer service incentives you want them to have. If you don't like the way a store treats you, you don't have to go back. But if you don't go back to Court, they can and will issue a warrant for your arrest. Like it or not, the Court is on top of this relationship. Get used to it.
Second, some courts have minimal resources. Upstate New York has hundreds of towns and villages with small populations (less than 1000 people and often much less). These communities can't afford to have full-time court staff. For many courts, the judge or clerk comes in once a week for a couple hours. They're not answering the phone because they're not there.
Third, the busiest courts are ... very busy. They have a full-time court staff, but they're overwhelmed by the volume of cases. Phone calls, while convenient for you, are inefficient for them. Your phone call will take five minutes where responding to a letter from you might only take two. Also, your letter goes into a stack and can be processed in an orderly fashion. Phone calls interrupt the work flow.
There are a few things you can do to deal with this situation. My most practical suggestion is that you find other ways to contact the Court. The best way, in my experience, is to fax a letter to the Court using a fax machine that prints a confirmation sheet. Our confirmation sheets even have a copy of the first page of the fax. It is very powerful to show this to a judge: "I really did send this letter in and this document shows that your Court received it." Regular mail is okay in most circumstances but courts do make mistakes and that fax confirmation sheet is great. Certified mail and FedEx are pretty good, but expensive and they don't have that copy of the document. Of course, some courts don't accept faxes. Remember what I said above about customer service incentives?
Another practical suggestion is that you should hire a lawyer. We deal with courts all the time. It might take you 5-10 hours of work (and a lot of frustration) to get your ticket resolved. The same thing might take us only 30 minutes or an hour. In most cases we will get you as good a result and often better. We know how the courts work. I actually get calls from people who think I have the secret phone number for the Court because the official number doesn't work. If I had it, do you really think I would give it to you?
My final suggestion is less practical for your current case, but more important for the long term. Make sure you vote. The reason courts are so busy is because there are so many tickets written, and so many other cases. This is all a result of the "tough on crime" attitude of so many candidates. What you've discovered in this case is that "tough on crime" means tough on you. Our system has always been aggressive about murderers and rapists. That harsh system is now spending most of its time going after speeders, marijuana smokers, and people who had one drink too many before they went home. You can change things. Look for candidates who are smart on crime and push the ones who aren't.