Model binary-choice decision from time-series data

I am looking for some suggestions for modeling the following decision-making problem:

Subjects had two choices when making a decision in a randomized control trial. The decision-making process can take several seconds. During the trial, time-series data (~10 Hz) from the subjects were recorded; these data usually slowly changed over time (mainly representing physical movements). I do not know the subject’s decision while performing the trial, but I know the decision at the end of every trial.

What I am after is a model of that binary-choice decision, which could also be used to predict the decision outcome (and ideally even its probability/uncertainty/timing) on new data at any given time. Any thoughts/suggestions (ideally incl. packages) are highly appreciated.