Pad Thai usually relies on tamarind paste for its unique flavor profile, but I think that the combination of lime and brown sugar accomplishes this well in this dish, without requiring that you search out and buy difficult-to-find ingredients. That said, if you have tamarind paste available to you, you can definitely use it here - simply reduce the brown sugar in the  sauce by 1 tablespoon and use only half the lime juice. Dissolve 1 tablespoon tamarind paste in ¼-cup warm water before adding it to the sauce. Do not add additional water.