Why (the heck) is the basic angle of GAIA 106.5°? This answer to Why does the Gaia space telescope have two main mirrors says:

According to the GAIA FAQs which does an excellent job: http://www.cosmos.esa.int/web/gaia/faqs:

Why is there an angle of 106.5 degrees between Gaia's 2 telescopes?
The choice of the so-called basic angle of GAIA was a non-trivial one. On the one hand, it should be of order 90 degrees to allow simultaneous measurements of stars separated by large angles on the sky. On the other hand, it should not be a harmonic ratio of a 360-degree circle (e.g., 60 deg, 90 deg, or 120 deg). Taking these considerations into account, acceptable ranges for the basic angle are 96.8 +/- 0.1 deg, 99.4 +/- 0.1 deg, 100.5 +/- 0.1 deg, 105.3 +/- 0.1 deg, 106.5 +/- 0.1 deg, 109.3 +/- 0.1 deg, 109.9 +/- 0.1 deg, etc. Accommodation aspects identified during industrial studies subsequently favoured 106.5 deg as the value finally adopted for Gaia.


I don't understand any of that.
Questions:

&quot;On the one hand, it should be of order 90 degrees to allow simultaneous measurements of stars separated by large angles on the sky.&quot; Well any large angle is a large angle, why should it be 90?
&quot;should not be a harmonic ratio of a 360-degree circle&quot; I can imagine for instrumental reasons, but why are &quot;acceptable ranges for the basic angle are 96.8 +/- 0.1 deg, 99.4 +/- 0.1 deg, 100.5 +/- 0.1 deg, 105.3 +/- 0.1 deg, 106.5 +/- 0.1 deg, 109.3 +/- 0.1 deg, 109.9 +/- 0.1 deg, etc.&quot; and what does &quot;etc.&quot; mean here? Is there a pattern I'm not seeing?

Any angle with an uncertainty of +/- 0.1 deg can be reached with some rational number with a denominator of 1800 or less, that's as far as I've gotten.
I did not find anything conclusive on the web, and I am yet waiting to receive feedback from ESA's contact page. In a German speaking IT forum there is something a bit less vague than the FAQ cited in the question:

The reason for the 106.5 degrees is not easy to see. It has to do with the fact that we are (also) doing an astrometric solution on a great circle and for this all angles 360x(n/m) [n, m = small integers] have to be avoided because otherwise one would have a congruence state that would hinder the solution. Values other than 106.5 degrees would also be possible. 90 degrees would be ideal for parallax determination, but unfortunately 90=360x(1/4).

This said, why not simply choosing 91° as $\gcd(360,91)=1$ (with $\gcd$ being the greatest common divisor)?
Maybe it is really only a numerology of the engineers, just like the Mars parachute Morse message. An argument for that would be that Gaia also has also exactly 106 CCD sensors. Or it is simply a logistical issue on how to mount things on the spacecraft. I am really curious what the official ESA statement will be.