Machine learning algorithm(s) for recognizing simple graph patterns
I suspect machine learning is the wrong approach.  Instead, I suspect you will do better to define a metric and measure the metric, or define a hypothesis and use hypothesis testing.  You are not trying to predict the future evolution of these values; that's something that ML might be suitable for, but that's not what you're trying to do, so ML doesn't seem like the right tool for the job.

Let me suggest an approach.  If $f(t),g(t)$ are the values of the measurements at time $t$, define $D(t) = |f(t)-g(t)|$ (the absolute value of the difference).  $D(t)$ measures how close they are.  Then, you want to test whether $D(t)$ is increasing or decreasing.  If $D(t)$ is decreasing, then you have a situation of "convergence"; if $D(t)$ is increasing, then you have a situation of "divergence".

How can you test whether $D(t)$ is increasing vs decreasing, over some time period?  Here's one simple approach.  You could separate your time window into two halves, the first half and the second half.  Calculate the average value of $D(t)$ over the first half, say $\mu_0$, and the average value of $D(t)$ over the second half, say $\mu_1$.  Now you can compare $\mu_0$ to $\mu_1$, to determine whether it is increasing or decreasing.

Alternatively, another approach would be to use simple linear regression on $D(t)$ to fit a linear model $D(t) \sim \alpha t + \beta$, and then test whether the slope $\alpha$ is greater than zero or smaller than zero.

However, one problem with this is that your conclusion might be confounded by noise: it might be that $D(t)$ is neither increasing nor decreasing, but all you're seeing is statistical noise.  So can you separate out the case where $D(t)$ is increasing from the case where $D(t)$ is decreasing?

The answer is yes: you can test for statistical significance using hypothesis testing.  If you observe $\mu_0 &gt; \mu_1$, you can use a hypothesis test to test whether this difference is statistically significant (e.g., using a permutation test).  Or, if you fit a linear model and find $\alpha &gt; 0$, you can use a hypothesis test to test whether the difference from zero is statistically significant (this is covered under standard textbooks on linear regression).

There's lots more one can say about hypothesis testing, but this should give you the general approach.  The short version is: don't use machine learning; using an appropriately chosen statistical measure or statistical hypothesis test.