Fields of the Nephilim formed in 1984, putting them definitely in the second wave of goth, as in a band that deliberately, from the outset, chose to be goth and remained so as part of a defined subculture.
As for points about goth and post-punk...goth IS post-punk. Joy Division were the first band ever to be referred to as 'gpthic'. The Cure and the Banshees were absolutely instrumental in defining goths look, with Robert Smith and Siouxsie Sioux being the male and female prototypes respectively. There is a sort of magic period between about 1980 and 1982 where what you call goth, post-punk or no-wave is really all a matter of personal taste in a lot of cases. I could certainly make the case that the Birthday Party were all three simultaneously. As for happiness in goth music...oh come on. You're kidding right? The veritable theme tune of the whole subculture is a novelty dub track about Bela Lugosi (and whether is dead, not dead or undead). The NME, still inflated by their success in the late 70's, tried to call the whole genre 'positive punk'. Like the previous 'Gothic revival' of the Mid 18th to early 19th century, and the better classic Universal Horror films, the whole thing was, indeed in the better circles is, really just a studied exercise in high camp and kitsch, with some great music and clothes thrown in. An excuse to drink absinthe by the bottle, dance like a broken street-sweeper and pretend to be a vampire in an atmisphere of comfortably disinterested artistic introspection. The real arseholes, the glum, over-serious forced depressives who view self-harm as a mark of status, who wear the black as a uniform, who seriously think that 'goth points' and other such satirical constructs actually exist, and think the Sisters of Mercy were being serious didn't turn up mostly until about 1990, and the really brutal perversions didn't come about until the whole concept started disseminating itself outside the major American cities in the (largely) pre-internet age. Goth is a state of mind more than anything, musical taste being somewhat important and fashion sense, in the scheme of things, the least...and the first and only rule is that a real goth never, ever calls themself goth unless they're joking.
Nu metal kiddies are about as far from the original denizens of the slimelight club as bonobo monkeys are from the Neitzschean ubermensch.