it seems your definition and mine share a few good points, but i'm defining "new" Goth Punk. not the "true" Goth Punk of the 70s and 80s.
Anyway, punks who dress like goths isn't really new. I'm thinking of Siouxsie Sioux and Dave Vanian, in particular... Then, there were the deathrockers--Christian Death, Shadow Project, etc. Sometimes the Misfits are included, sometimes not.
By the way, it may be worth mentioning that Trent Reznor and Marilyn Manson claim Rozz Williams was an influence on their work.
Musically, the term goth punk today helps define the sound of bands that have an old school hardcore punk (aka street punk or Thrash) sound with dark lyrics and optionally added keyboard/symphonic samples and electronics. Since goth has strayed away from its punk roots with the rise of Nu-Metal, EBM, and Emo-Pop, the rebellious reaction is more extremely "punk" style goth bands arising in the underground.
-Love Equals Death
Usually, the goth punk can be identified by a very zombiefied appearance; mixing punk and goth with a heavy DiY (do-it-yourself) ethic. Their attire usually consists of layers of torn black, white, and green fishnets, heavy combat boots, ripped t-shirts, leather pants or bleached jeans, and a leather jacket/vest full of band patches, studs, designs, plastic bones, etc. Many of them have huge, teased hair, and a very popular style for both men and women is the death-hawk, a wider, teased version of the mohawk.
Goth punks (or deathrockers) can be thought of as the missing link between goth and punk. They're not any more rambunctious or outspoken than regular goths or punks; they just have different tastes.
Keep in mind that there were also several 'dark punk' bands around the same time that, while not maybe being quite as 'gothic' in some regards, still had enough stylistic similarities to be worthy of mention. They include bands such as: The Adicts, The Adverts, The Mob, False Prophets, Wipers, Chrome and can't forget classics that bridged the gap between hardcore and darkpunk such as Black Flag, Dead Kennedys and The Misfits. One should at least check out the classic goth punk (or, as I prefer to call them, deathrock) bands before making comments on the genre. Keep in mind that while all these bands have similarities, they also have very distinctive sounds that set them apart from the others, as all good artists should, so don't think that just because you've heard one or two of the bands mentioned that you know what goth punk sounds like. Modern goth punk bands worthy of mention are: Cinema Strange and Cauda Pavonis.