I am playing an unbodied, I had some trouble with the GM about what happens in an anti-magic field. I believe that since there is no comma, and no "and" between "incorporeal" and "undead" in the sentence "Summoned creatures of any type and incorporeal undead wink out if they enter an anti-magic field" It would not affect Undead nor incorporeal but only incorporeal undead while he does not, this is D&D 3.5.
Later on it says "Elementals, corporeal undead, and outsiders are likewise unaffected unless summoned." This clarifying statement confirms that the usage of "incorporeal undead" as a singular noun. Additionally I wouldn't consider an unbodied as an undead type as it is a psionic type so in looking at the overall concept of an anti magic field, an unbodied would not be affected.
Rules Compendium updated the antimagic rules; incorporeal creatures disappear in AMF. (RC, p.11)
Summoned creatures of any type disappear if they enter an antimagic area. Incorporeal creatures do the same. These creatures reappear in the same spot once the antimagic effect goes away, unless they were summoned by an effect whose duration has expired—see Spells, below
Additionally, the original RAW does indeed only mention incorporeal versus corporeal undead, but the difference is the incorporeality. That difference could show rules intent that it's the incorporeal nature of the creature that causes its disappearance. In the non-psionic portion of the SRD, AKA the core rulebooks, only undead are incorporeal, so the authors and editors at the time appear to have overlooked that it was possible to have living incorporeal creatures. The DM has a leg to stand on mechanically, and thematically as well.
Interestingly, incorporeality is unmentioned in Null Psionics Field, even though they kept the phrasing "...corporeal undead...", with the emphasis being mine.
[unrelated to question re:unbodied; I'd originally misread unbodied as uncarnate] Psion Uncarnate's 10th ability (Uncarnate) is listed as (Ex), however, so DM adjudication (fiat) might be needed, as Ex abilities continue to function in AMF. If your DM says you're Good To Go, get the ghostly grasp feat (Libris Mortis) if you're planning on doing much in an AMF.[/unrelated]