I don't have a lot of time either Dapper, but you've brought up a good point.
For me being third gender, I don't think of myself as transgender so much, mostly because I feel myself as being of both sexes/genders... and that to me feels quite different than what I understand to be most TG experiences of feeling like the "opposite gender/sex in mind than in one is in body".
Third gender to me is difficult to explain, b/c in it like you, I'm not a woman and I'm not a man (gender)... but find my myself both male and female... and though I acknowledge my body as female and that's fine, I do tweak my body (bind etc. though I'm small chested already) to better fit my gender.
Anyway, to me that's a fairly big distinction, and why I (personally) separate transgender and third gender personally for myself... though I do know a couple peeps who do like you ID as TG as well in it.
So I go with the "similar, yet different" option... with overlap...
As far as genderqueer I think of it kind of an umbrella term and works for many TG and Third G peeps, but I don't use it myself because of that vagueness.
Right, genderless or gender neutral generally means being of an indifferential gender, and may feel gender "empty" and wear ambiguous, or gender vague clothing... think the gender neutral lesbian feminist type that emerged in the 70's and 80's.
That's not the same thing I've seen at all with most modern third gender (or pangender's Androgyne's) peeps or especially of the butch variety who consider themselves Third G or Other.
I know I feel quite the opposite of genderless, more like genderfull, having strong gender traits of both sexes psychologically and outwardly very strong gender markers (male) in my clothing and mannerisms.
Ok, have to run... pls forgive the loose exchanges of sex with gender but it's hard to navigate the subject with a language not set up to accommodate additional gender/s.