You can. Your pick-up truck can qualify for passenger class plates if it meets certain conditions, depending on its unladen weight.
In addition, I need to inquire about proof of sales tax payment.  What should I do if at the time of the purchase of my vehicle I was not a resident of NYS?
In that case please use the Sales Tax Exemption Form {Sales Tax Form} pdf at the New York State Department of Taxation and Finance DTF-803 to receive a - Resident Exemption from Sales Tax New York State. Form DTF-803 defines the terms "non-resident" and "resident".
What if the person is a member of the United States Armed Forces and does not reside in New York?