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Having just watched the movie "First Man," I'm interested in analyzing the Gemini 8 malfunction in physics terms and possibly turning it into a homework problem or an example for my physics classes. I would like to get the facts right and get the numerical data as accurate as possible. There was some kind of board of inquiry afterward, and I would imagine that its findings are available somewhere online, presumably with engineering data and reconstructions, but WP doesn't link to any such document. Is there such a thing that is accessible to the public?

WP says, "By now the tumble rate had reached one revolution per second, blurring the astronauts' vision and threatening loss of consciousness or vertigo." In the film, there is a dial that goes up to 360, and the needle appears to be pinned at the moment of fastest rotation. I assume that this is in units of degrees per second. Is there any more accurate value available for the maximum rate of rotation?

WP describes the motion as a yaw, which I assume means a yaw in a coordinate system oriented according to the way the astronauts were seated in the Gemini capsule. Did it continue to be a pure yaw after decoupling from the Agena, presumably because it was being caused by a yaw thruster on the Gemini capsule?

How far were the astronauts from the yaw axis? From this NASA artwork, my best guess is that each astronaut's heart was something like 40 or 50 cm away from the yaw axis, i.e., where the cup holders would be in a modern car, but it's pretty hard to tell for sure. An engineering drawing would probably allow this to be determined much more accurately.

Using a period of rotation of 1 second and $r=45 textcm$, I get an acceleration of $1.8g$. Is this in the right ballpark for the effects described in the WP quote? I would imagine that a sideways acceleration like this would be somewhat less dire than an upward acceleration, which would prevent blood from getting to the brain.

A more authoritative source than Wikipedia would be NASA's Gemini VII Mission Report. Starting on page 5-25, the anomaly is described, with the main effect being an uncontrolled roll peaking at somewhat less than one revolution per second rather than Wikipedia's yaw:

Separation from the GATV [Agena] occurred at 7:15:12.3 GET with thrus­ters ll and 12 firing for 6.6 seconds. Rates at this time were +3, -5, and -2 deg/sec in pitch, roll, and yaw, respectively. After separation, moderate hand-controller activity was present, although the direct mode was not sufficient to contain the roll rate. At 7:15:44.7 GET, the ACME bias power was inadvertantly removed, dis­abling the control system, and the roll rate increased to 296 deg/sec over the next three minutes, due to the uncontrolled firing of thruster 8, although short periods of intermittent or degraded thruster 8 performance appeared to exist.

The roll axis is of course the longitudinal axis of the spacecraft; a seated astronaut facing forward in the Gemini couch is looking parallel to the roll axis.

The Gemini cockpit was quite cramped; picture the front seats of a small roadster, not an SUV. The couches are canted slightly apart from each other:

...so the roll axis passes not far from each astronaut's inboard hip -- your 45cm axis-to-heart estimate seems plausible, though with a high roll rate, excessive blood flow to the head would seem the more pressing problem, and the radius of concern might be more like 1 meter (the spacecraft being 3m in diameter)... although, mumble, acceleration gradient, calculus, grumble grumble

The crew debriefing document is also available, with more subjective impressions of the incident; Armstrong and Scott mention yaw but confirm the primary mode was roll:

Armstrong: Shortly after backing off, we noticed that we were essentially losing control of the spacecraft in roll and yaw and we suspected that we were over the life­ time of these attitude thrusters. The spacecraft was continuing, however, to accelerate, and we were ob­taining rates in roll at least that approached 200 to
300 degrees per second, or perhaps more.

Scott: Yes, I would agree with that. It looked like even more to me, and it was by far more in roll than in yaw. The roll was the most predominate. [sic]

Armstrong: We realized that physiological limits were being ap­proached, and that we were going to have to do some­thing immediately, in order to salvage the situation.

(You’ve got to love that professional detachment!)