When we plot the path $\gamma(t):= \zeta (\frac 12+it)$ starting at $t=0$ and letting $t$ increase, we get the following beautiful image (courtesy of 3b1b's Riemann zeta function video's thumbnail), where $t=0$ corresponds to the point at around $-1.4\in \mathbb R$. As you can see, as $t$ increases, the path $\gamma$ starts with a counterclockwise orientation, until it reaches $t\approx 2.75648838$ where "first and second derivatives of f(t) are parallel" according to https://www.reddit.com/r/askmath/comments/mm15aq/comment/gtqlvqh/?utm_source=share&utm_medium=web2x&context=3), at which point it switches to being clockwise forever (as least as far as all animations I've seen go).
Here's a video https://www.youtube.com/watch?v=6xcWykLZ2rw&ab_channel=UnintendedConsequences in which you can see the curve $\gamma$ animated, as well as related curves $t \mapsto \zeta(a+it)$ for $a=\frac 13, \frac 23$, etc. (start at minute 2:10 and 4:10 for related curves --- it's remarkable that the related curves "keep pace with each other" so well, e.g. the points $\zeta(\frac 13+it), \zeta(\frac 12+it), \zeta(\frac 23 + it)$ are almost collinear for all $t\in \mathbb R$!).
A similar behavior (counterclockwise until $t \approx 2 \pi$, and then clockwise forever afterward) appears in the plot of $t\mapsto \frac{\zeta(a+it)}{\zeta((1-a)-it))}$ (expressible as product of exponential, sine, and Gamma factors by the functional equation) as in minute 12:40 of the above mentioned video. It is also a bit unexpected to see the paths $\Upsilon_a(t):= \frac{\zeta(a+it)}{\zeta((1-a)-it))}$ seemingly ALL MEET at the counterclockwise-to-clockwise crossover/inflection point (as before, for fixed $t$, the points $\Upsilon_a(t)$ are almost collinear).
Primary question: is it proven that these paths $\gamma_a,\Upsilon_a$ are eventually forever clockwise (with the only inflection point appearing super early, as seen in the animations above)? If not, is this conjecture related to any better-known conjectures about the Riemann zeta function?
Any thoughts on the secondary questions (the simultaneous(?) and only(?) concurrence of the $\Upsilon_a$ curves at $t \approx 2\pi$; and almost collinearity discussed above) are also appreciated.
EDIT: https://mathoverflow.net/questions/309788/analogues-of-the-riemann-zeta-function-that-are-more-computationally-tractable mentions an function $S(t):= \pi^{-1} \arg \zeta(\frac 12+it)$ related to winding numbers of $\gamma$, which apparently Selberg proved in 1946 to be unbounded. Seems highly relevant to this question... however I can't find Selberg's 1946 paper, nor any references to this $S$ function.
P.S. another natural conjecture to have when watching the animations, is whether or not $\gamma$ hits the negative real axis other than at $t=0$. It does in fact; see https://mathoverflow.net/questions/73098/negative-values-of-riemann-zeta-function-on-the-critical-line.