Testing a javascript mutex implementation

I have written a mutex implementation for javascript / typescript, but I'm struggling with the question of how to test it. Here's the implementation:

class Mutex {

    private current = Promise.resolve();

    async acquire() {
        let release: () => void;
        const next = new Promise<void>(resolve => {
            release = () => { resolve(); };
        });
        const waiter = this.current.then(() => release);
        this.current = next;
        return await waiter;
    }

}

Usage:

const mut = new Mutex();

async function usesMutex() {
  const unlock = await mut.acquire();
  try {
    await doSomeStuff();
    await doOtherStuff();
  } finally {
    unlock();
  }
}

I'm not sure if there's any easy way to create the sort of timing issues that would lead to a test failure if the mutex doesn't work as expected. Any advice would be very much appreciated.