Lyric discussion by putto 

Cover art for Your Bruise lyrics by Death Cab for Cutie

I like to think of "forward" as in "lacking restraint or modesty; presumptuous or bold" rather than looking to the future. Her eyes are being forward with him.

Oh and for those that think they're sailing the high seas, here's what a Plymouth is: http://en.wikipedia.org/wiki/Plymouth_%28automobile%29