You highlight a very important point UD,
Customer service, most especially when Drop-shipping, is one of the key factors people should consider when deciding who to do business with. If a supplier provides you with an undervalued level of service when there is no pressure to resolve an issue, then what level of service can you expect when there is pressure?
So for my money, Customer Service is right at the very top of my list when I do business with anyone. That goes hand in hand with method of contact. I always look for multiple contact options, not just an email option so if the first option isn't getting a response, there are multiple options available for me to reach out and I am not sitting there hammering away email after email and getting nowhere.
A support contact number is great, but at the very least every supplier with any sense of providing quality customer service will have a Social Media profile and even live online support for service inquiries at the very least. If a supplier isn't switched on enough to offer that limited, but effective level of Customer Support options, then they wouldn't make my list of possibles.
Suppliers who don't make it easy to contact them usually have a reason. Now that doesn't mean they are not legit, but ignorance in business can be just as damaging to customers.
So things like this are extremely important to consider when choosing a supplier. If they don't provide you with quality Customer Service, then how on earth will you be able to provide that quality of service to your customers?