(written from a Production point of view)
The thruster suit was envisioned as a variation of an environmental suit, that could be equipped with a detachable thruster pack for use to travel short distances, and has been seen in use in Star Trek: The Motion Picture by, among others, Starfleet personnel at the Epsilon IX station as well as the drydock were the upgraded USS Enterprise was refurbished. Equipped with the thruster pack, Spock utilized such a suit when entering and exploring the V'Ger entity in the early 2270s, whereas James T. Kirk subsequently used a thruster suit to retrieve Spock. The design of the suit was re-utilized in Star Trek II: The Wrath of Khan. Though full-scale suits were manufactured for the actors to interact with in The Motion Picture, they themselves soldiering on in The Wrath of Khan, the construction of a miniature was deemed necessary for The Motion Picture.
An extravehicular activity was already envisioned in a final draft of the "In Thy Image" pilot episode of the eventually abandoned Star Trek: Phase II television project. While in the employ of Robert Abel & Associates, Production Illustrator Andrew Probert submitted some preliminary design work for the environmental suit in October 1978. Unfortunately for him, Abel was pulled from the project when the production was upgraded to a feature film project in early 1979. Succeeded by Douglas Trumbull's Future General Corporation, it was decided to fine tune the spacesuit design at John Dykstra's Apogee, Inc., when that company was brought in to ease the workload, since a first appearance of the suit was envisioned in a sequence Apogee was responsible for, to wit, the Epsilon IX station footage.
At Apogee, Production Illustrator Jack Johnson took over the task of designing the suit as well as that of the thruster pack that could be optionally attached to it. Details on the suit were designed by Animation and Graphics Artist Greg Wilzbach. It was their envisioned versions that were predominantly featured in The Motion Picture. Johnson was also the one who designed the thruster pack unit. (The Art of Star Trek, pp. 180-181)
Apart from having full scale suits made for the actors to interact with, a scaled miniature was deemed necessary for the long shots. That miniature was also constructed at Apogee, and Dykstra has elaborated,
"Another thing we did for the Epsilon 9 sequence was build a two-foot tall scale model spaceman that we had zipping around this way and that. Doug used it also in the drydock sequence and in the Spock spacewalk. David Sosalla did the sculpting, including the faces of Spock and the others who would be inside the suit; and John Ramsay worked out the mechanics for articulating the arms and legs. It was shot using motion control, and then we went back in with animation and added little blips of energy from the thrusters.(...)
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"There were a couple nice shots that didn't get into the film, where the puppets are being chased by the destruction in a different way than we've got them appearing now. But we ran out of time, and weren't able to get them to go together right."For their appearances, Sosalla sculpted several heads for representation of whomever was supposed to be in the suit. The models themselves were equipped with servo motors and electronics for articulation. (Cinefex, issue 2, pp. 58-59)
Painted with orange highlights, the miniature was first used to shoot the sequences of the unfortunate Starfleet member caught in the digitizing of the Epsilon IX station and Spock's spacewalk in V'Ger. Subsequently, the highlights were repainted brown/beige for the sequences in the drydock and Kirk's EV scenes.
The miniature made an almost undiscernible re-appearance in Star Trek III: The Search for Spock as a display model in the Starfleet Officer's Lounge entry room, in the scene where Admiral Kirk and company leave.
After its use in The Search for Spock, the miniature was stored away on the Paramount Pictures lot and largely forgotten about, until Probert and Rick Sternbach rediscovered it. As the latter remembered, "If I recall correctly, when Andy was painting the head to look like himself, the rest of the suit hardshell was the orange color (early 1987?). I think we found the thing in a box in a storage room in the art department shortly after Andy and I commandeered the room over Stages 8/9. We had originally done some work in another office on the west side of the lot, but since the room over 8/9 was empty, we basically took it over. Anyhow, I’m wondering if the motor hardware was they way it was because the appendage moves had to be repeatable to within a very small tolerance, and the stepper motors I’ve seen are rather brutish to begin with. Steppers aren’t like "normal" spinning electric motors, for folks who aren’t familiar with them; the shafts are commanded to move in precise steps by motion control computers." 
"Anyone who has watched TMP remembers the little space guy who goes ass-over-tea kettle at Epsilon 9. If you run that back you will see the puppet articulate a tad as it is hit by the Vger wave. That’s probably all the range it had. A post mortem reveals why. Most of you know that I was an effects makeup artist for ten years. In them time I built my share of puppets and change-o heads. If I had been there when this fabricated, I might have saved them a lot of grief. When you take it apart you find an impressive dual cylinder piston driven motor, which probably could have driven a mini bike. All of that horsepower was to no avail. The rubber that the suit was cast from was much too rigid for an articulated puppet. Even with all of that power behind it. I’m sure one of you guys will know the answer to this, but my guess would be that it was built by a physical effects house that may not have had a lot of puppet building experience.The pictures Drexler showcased on his blog entry revealed that some of the second paint layer had chipped off over time, revealing in some places the original orange paint layer. This may have led to Sternbach's partially erroneous recollection in regard to the color of the miniature.
"All due respects to my physical effects brothers, but most of them are all about raw power. I’m guessing they were fairly certain that even though the cast was semi rigid they thought they could jam enough hp in there to make it work. I had a phys effects buddy who used to live by the adage, “don’t force it! get a bigger hammer!” By the time they found that the bigger hammer wouldn’t do it, it was too late to go back. If a makeup artist had built this rig, the appendages would have been made out of a fine cellular foam latex. if it had been me, I would have used the same foam latex we use for facial appliances. Extremly soft, malleable, great memory, and supremely paintable. If foam latex had been used you could have thrown all that expensive horsepower away. Just go to your local bicycle shop and pick up some el cheapo cables and levers, and this thing would’ve been able to dance like one of the Nicholas Brothers."
Drexler eventually auctioned off his miniature, sans thruster pack, measuring 11×25 inches, as Lot 11 in the Propworx's The official STAR TREK prop and costume auction of 8 August 2010, estimated at US$8,000-$10,000, where it sold for US$8,000. According to the auction description it was the miniature that represented Admiral James T. Kirk when he retrieved Spock in the movie.
Coincidentally, Spock's thruster pack miniature, constructed out of fiberglass, metal and resin and measuring 15½ inches long, had been shortly before offered up at Profiles in History's 8-9 October 2009 Hollywood Auction 37 as Lot 611. Having been estimated at US$6,000–8,000.00, it went unsold.