Seeing as I myself believe that I am one and am told I am one then perhaps I may be able to define the term more appropriately.
Emo Goth or Emo-Goth (other variations include Gothmo, Gothymo, Emoth and Emothic) Basically a cross between the subcultures of Emo and Goth, generally having dark views and opinions, being open to a variety of things, not being afraid of others differences and being in touch with their emotional side.
Personality: Tends to have a darker view of things in life, typically in art, clothing, poetry, and music. Tend to be very intelligent and analytical, but also very in touch with their feelings and emotions. Generally kind and honest and very open and expressive, although most have some secrets as well as others. May have any sexual orientation. Typically very romantic. May often appear sad, gloomy or depressed. Most are not like this however. On occasion they are depressed, generally as a reaction to something not-so-great that occurred in their lives. Some share the loving approachable characteristic of the Emo subculture. May possess a fascination with Death, spirituality, religion, vampires, etc., generally associated with the Goth subculture. Most possess a general spirit of defiance against conformity. Many don't care what the rest of the world thinks about them and don't. Most are not afraid to cry and dont see crying as weakness. Some may have a potential towards self-mutilation or suicide, but this is generally more prevalent amongst the posers of this culture.
Appearance: May possess traits of both the Emo and Gothic subcultures. May have Emo hair, typically parted to one side with a fringe that may or may not be in their face. May wear eyeliner or nail polish. May dress in clothing and attire from Hot Topic and Spencer's. May not. Typically mixed in with clothing from other such retail stores as Pacsun. Such attire may consist of alot of black, fishnet, trench coats, tight jeans, bondage pants, band tees , fingerless gloves, etc. Note that not all attire themselves in this fashion and some influences of one of the particular subcultures may be more prevalent.
Typically anything of a dark or romantic view. Gothic or Romantic Literature, novels and Poetry tend to be most common.
Generally widely varying, but it tends to have some common ground. Most Emo Goth's tend to like dark, sad, romantic music. Some may also have a tendency towards metal and death metal, but not all do. Typical Genres may include: Gothic, Emo, Grunge, Post-Punk, Post-Grunge, Nu-Metal, Pop Punk, Death Metal, New Wave, Ambient, etc. Basically anything they like they will listen to.
Some tend to look like Goth's with Emo hair. Or dress in an Emo fashion but with much more black.
Listing of typical Emo Goth poets/novelists:
Edgar Allen Poe, Anne Rice, Mary Shelley, Percy Bysshe Shelley, Lord Byron, John Keats, Stephen King, Dean Koontz, etc.
The bands which seem to be most widely listened to by the culture seems to vary, mostly by age. Older Emo Goth's tend more towards The Cure, Interpol, Depeche Mode, Siouxie and the Banshees, Nirvana and Jimmy Eat World whereas younger Emo-Goth's may listen to those bands as well as more recent acts such as My Chemical Romance, Aiden, AFI, Taking Back Sunday and Deftones amongst other things. Generally the younger generation is open to a broader range of music.
In depth listing of bands that are oft times listened to by Emo Goths:(not necessarily always, and there are others besides these)
30 Seconds to Mars, AC/DC, Action Action, Adema, AFI, Aiden, Alice In Chains, Alkaline Trio, Atreyu, Avenged Sevenfold, Bauhaus, The Beatles, Beck, Black Sabbath, Blink 182, Blood Brothers, Breaking Benjamin, Bright Eyes, Bullet For My Valentine, Bush, Cake, Calico System, Chevelle, Chiodos, The Clash, Coheed and Cambria, Coldplay, Crossfade, The Cure, Death Cab for Cutie, The Deftones, Depeche Mode, Disturbed, The Doors, Drowning Pool, Evanescence, Faith No More, Fear Factory, Foo Fighters, Franz Ferdinand, Freeze Pop, From First to Last, Funeral for a Friend, Godsmack, Goo Goo Dolls, Green Day, Hawthorne Heights, Hellogoodbye, HIM, Hot Hot Heat, Interpol, Iron Maiden, Jack's Mannequin, Jane's Addiction, Jet, Jimmy Eat World, Joy Division, The Juliana Theory, The Killers, Killswitch Engage, The Kinks, Lacuna Coil, Lamb of Gob, Led Zeppelin, Marilyn Manson, Matchbook Romance, Matchbox 20, Metallica, Modest Mouse, Mudvayne, Murderdolls, Muse, My Bloody Valentine, My Chemical Romance, My Mourning Jacket, Neon Blonde, Nine Inch Nails, Nirvana, Oasis, Ozzy Osbourne, Panic! At the Disco, Pantera, Papa Roach, Pearl Jam, A Perfect Circle, Pink Floyd, The Police, Powerman 5000, Pretty Girls Make Graves, Puddle of Mudd, Queen, Queens of the Stone Age, Rage Against the Machine, The Ramones, The Red Hot Chili Peppers, Rise Against, Rolling Stones, Seether, She Wants Revenge, Shinedown, Shiny Toy Guns, Siouxie and the Banshees, Sisters of Mercy, Slipknot, Smashing Pumpkins, Stabbing Westward, Staind, Story of the Year, STP, Streetlight Manifesto, The Strokes, System of a Down, Taking Back Sunday, Three Days Grace, Thrice, Thursday, Tool, Underoath, The Used, Velvet Revolver, We Are Scientists, Weezer, The Who, White Stripes, White Zombie, The Yeah Yeah Yeahs, and Zeromancer
A contradiction of terms as emos will piss moan and cry about their plush lifestyles only to cut and cry to themselves over and over again for not getting what they want or even because they simply feel like it While goths simply do not care about their lives as they hate everything and simply cut for the sheer release and thrill it brings but will not cry to themselves in the corner.
Emos envy the goths for their lack of crying and thus try to imitate their sub culture by wearing similar fashions, but are easily spotted as they will often be seen crying to themselves over every pathetic little thing especially if it affects their selfish and overly comfortable lives and will put on massive drama shows that effectively annoy all around them until they gt what they want.
Goths usually wear dark clothes and make-up with practiced fervor and are also clearly distinguishable as they will glare at you and refuse to shed tears over anything while living a more minimalistic and death-centric lifestyle, after all you can't take possessions with you when you die and will usually keep to themselves as they have no desire to interact with others.
Due to the contradictions between the two as far as outlooks and reactions emo-goths do not exist
Impossible to define an emo-goth as both are polar opposites that the only similarity is in how they dress, Simply put if both were a magnet Emo would be south and Goth would be North