By stochastic, I mean it randomly ticks on only one arbitrary beat per measure
Well, something like this is actually quite popular in modular synthesizers community. They have one type of modules called “Clock generators” which generate gate/trigger signals for given BPM (Like 1/4 or 1/8 or 1/16 rhythmic pulses for 120 BPM for example) and another type of modules called “Bernoulli gates”, which basically allow to specify probability of input signal going to the output. Those beat-skipping metronomes with configured probabilities are then used to trigger notes or samples or whatever. Also, this is modular where you can modulate almost everything, including BPM itself, but that’s a different story… Stochastic music approaches like this are often called “alleatoric music”.