In a similar vein as this question, can an elemental bound item, such as would be created by the Bind Elemental Feat or other related concept, such as a Nimblewright (a construct possessed by an elemental spirit) be a valid target for the psionic powers mind seed, mind switch, true mind switch, or similar effects?
The Monster Manual description of the golem says
The animating force for a golem is a spirit from the Elemental Plane of Earth. The process of creating the golem binds the unwilling spirit to the artificial body and subjects it to the will of the golem’s creator. (134)
Similarly, the Monster Manual III description of the nimblewright says
Like a golem, a nimblewright is a powerful creation that combines awesome magic with elemental forces. Its animating force is a spirit from the Elemental Plane of Water. The process of creating a nimblewright binds the unwilling spirit to the artificial body and subjects it to the will of the creator. (163)
Thus, prior to such constructs' creation, there are just parts and a free spirit, and it's the construction process that makes the spirit and artificial body one being, giving the collective entity the type construct, and it's that construct type that grants immunity to mind-affecting effects, vastly limiting the ability of most of the powers in question to target the resultant magical robot.
Were a DM to rule that the elemental spirit could be affected separately—that the elemental spirit were more than just an intangible, undetectable battery that enables the construct to move and follow commands and that the spirit were, instead, its own independent creature yet trapped in the construct shell—there's still a matter of targeting the elemental spirit. Even the 9th-level telepath power true mind switch [telepathy] (Expanded Psionics Handbook 120) requires line of sight and line of effect, and—so far as I'm aware—there's no way to get line or sight or line of effect to the creature's animating force. Similar to how a typical creature can't opt to cast the spell magic missile at—or poke a sword at!— his foe's soul, a creature can't opt to target with the power true mind switch a golem's animating force—even if the attacker knows there's a soul or animating force in there somewhere! (A DM would have to rule that, like, golems and other such creatures literally wear their hearts on their sleeves for this to be a thing.) (Spells that target a golemlike creature's animating force would likely have to be the product of original spell research—see Dungeon Master's Guide 198.)
(Also, keep in mind that the game offers no further description of the elemental spirits that are bound to such constructs. Any DM that decides to make this a plot point must homebrew such spirits.)
The feat Bind Elemental (Eberron Campaign Setting 51) has a description that runs only about 200 words, significant for a feat but not overwhelming. However, Magic of Eberron actually describes what it means to employ the feat Bind Elemental… and that takes over 2,700 words (from pages 11 to 14 including details on elemental vessel binding). In short, what happens when an elemental is bound using the feat Bind Elemental is that the elemental is shrunken and confined within a Khyber dragonshard in which it zips around endlessly, powering the magic item to which its attached. While the shard remains intact, establishing line of sight and line of effect to the elemental within is virtually impossible. (Even for vessels powered by bound elementals, "[t]o establish line of effect with a bound elemental, you must be touching the dragonshard to which the elemental is bound" (Explorer's Handbook 26), but the only effects that are listed as being usable due to that line of effect are charm, dominate, and elemental command via rebuking.)
Now, I guess, in theory, using an effect like the 4th-level Sor/Wiz spell scrying [div] (PH 274-5) a caster could peek in on the elemental to make sure the elemental's in there then—probably, somehow, likely with the 5th-level Sor/Wiz spell magic jar [necro] (PH 250-1) with its substantial differences from the psionic powers the question mentions—swap souls with the elemental, but then the caster would find himself trapped in the Khyber dragonshard!
What happens next is GM fiat, but this DM would likely have the caster find himself forced to zip around powering whatever it is the bound elemental was powering. This sounds like the last desperate act of cornered wizard and an excellent plot hook, but—like the 9th-level Pain domain spell eternity of torture [necro] (BV 93-4)—a really terrible way of living forever.
Mind Seed, no. Mind Switch, sort of
Mind Switch targets "a nearby living creature". True Mind Switch inherits that without modification. Mind Seed must target "One touched Medium or smaller humanoid". Elementals qualify as living but not humanoid, and nothing about being bound into an object changes that. Now, as a bound elemental, your ability to act is likely to be limited, and, I believe, you'd be blind. Still, yes, it should be possible.
In particular, it would be entirely possible to mind switch into an elemental, and then, as that elemental, be bound into an object. There's no particular reason to think that you could not do that in the opposite order, and it's certainly possible to get within range close. Certain kinds of elemental bindings might fully surround the elemental within a casing, which might raise line of sight or line of effect issues, but not all of them. Mind Seed's requirement of touch isn't an issue due to having already failed the humanoid requirement.
To address an issue raised in the comments, even elementals bound into items still exist as entities capable of thought and potentially capable of being targeted. A quote from a sidebar in the Eberron Campaign Guide, page 267:
In order to make the elemental obey any of these commands, an unmarked character must win an opposed Charisma check against the elemental (virtually all elementals have a Charisma modifier of +0). If the elemental wins the opposed check, it either continues with the current course of movement or brings the vehicle to an immediate stop, according to its whim. If the character wins the opposed check, the vessel moves as the character intends.
It is noted somewhat later in the sidebar text that a spell of Charm Monster also does the trick of keeping control of the vessel. Thus, the elemental is capable of some degree of agency even without direction (though quite limited) and can be targeted by mind-affecting abilities (cast by people who are touching the control stone). Nothing stops Mind Switch other than a desire to not be a bound elemental.
For the nimblewright, there are a couple of problems. Quote from MM2, page 162-163:
The process of creating a nimblewright binds the unwilling spirit to the artificial body and subjects it to the will of the creator
Thus, even if you could get line of effect on the bound elemental, you would be mindswitching into an elemental that is already bound, and the implication is that it is the fact of being bound to the nimblewright that subjects the elemental to the will of the creator. That's supported by the fact that the nimblewright retains the full suite of construct traits, including the immunity to mind-affecting abilities.