I made this visualization of the zeta function in javascript, it is infinitely zoomable, and you can play around with parameters: https://amirhirsch.com/zeta/index.html
It might help you understand why the hypothesis is probably true. It renders the partial sums and traces the path of zeta.
In my rendering, I include all partial sums up to an automatically computed "N-critical" which is when the phase difference between two summands is less than pi (nyquist limit!), after which the behavior of the partial sums is monotonic. The clusters are like alias modes that go back and forth when the instantaneous frequency of the summands is between kpi and (k+1)pi, and the random walk section is where you only have one point per alias-mode. The green lines highlight a symmetry of the partial sums, where the clusters maintain symmetry with the random walk section, this symmetry is summarized pretty well in this paper: https://arxiv.org/pdf/1507.07631
I formed an intuitive signal processing interpretation of the Riemann Hypothesis many years ago, which I'll try to summarize briefly here. You can think of the Zeta function as a log-time sampler -- zeta(s) is the Laplace transform of sum(delta(t-ln n)) which samples at time t=(ln n) for integers n>0, a rapidly increasing sample rate. You can imagine this as an impulse response coming from a black box, and the impulse response can either be finite in energy or a power signal depending on the real parameter.
If you suppose that the energy sum(|1/s|^2) is finite (ie real(s) > 1/2), then the Riemann Hypothesis implies that the sum is non-zero. It is akin to saying that the logarithmic sampler cannot destroy information without being plugged-in.
For the longest time I thought the zeta curve was some kind of sophisticated equation, but it is astonishingly simple. The "magic" of the zeta zeros only happens because of the 1/2 term in the exponent of the equation below. Any change with this fraction, and the zeros do not converge.
You start with a line segment. You then draw another line segment that starts at the end of the previous line segment, and whose length is shorter than the previous segment. The length of any segment is (1/n)^(1/2) where n is the number of the segment. These segments approach a limit (think of Zeno's paradox).
Finally, you bend each segment by an angle alpha. Technically this angle is in imaginary space, but the visual in Cartesian space just looks like a spiral, where each bend adds an angle, like a bull whip, so that the whole curve spirals back around (after creating other, mesmerizing sub-spirals). Amazingly, this curve always intersects zero (per Riemann Hypothesis). As I mentioned in my other comment, it's very useful to see this curve in 3D space.
It might help you understand why the hypothesis is probably true. It renders the partial sums and traces the path of zeta.
In my rendering, I include all partial sums up to an automatically computed "N-critical" which is when the phase difference between two summands is less than pi (nyquist limit!), after which the behavior of the partial sums is monotonic. The clusters are like alias modes that go back and forth when the instantaneous frequency of the summands is between kpi and (k+1)pi, and the random walk section is where you only have one point per alias-mode. The green lines highlight a symmetry of the partial sums, where the clusters maintain symmetry with the random walk section, this symmetry is summarized pretty well in this paper: https://arxiv.org/pdf/1507.07631