How to have a WPF binding update every second?

You could create a single DispatcherTimer statically for your view model, and then have all instances of that view model listen to the Tick event.

public class YourViewModel
{
    private static readonly DispatcherTimer _timer;

    static YourViewModel()
    {
        //create and configure timer here to tick every second
    }

    public YourViewModel()
    {
        _timer.Tick += (s, e) => OnPropertyChanged("SecondsSinceOccurence");
    }
}

A purely MVVM sulution

Usage

<Label xmlns:b="clr-namespace:Lloyd.Shared.Behaviors"
       xmlns:i="http://schemas.microsoft.com/expression/2010/interactivity"
       Content="{Binding MyContent}" Width="80" Foreground="{Binding MyColor}">
    <i:Interaction.Behaviors>
        <b:PeriodicBindingUpdateBehavior Interval="0:00:01" Property="{x:Static ContentControl.ContentProperty}" Mode="UpdateTarget" />
        <b:PeriodicBindingUpdateBehavior Interval="0:00:01" Property="{x:Static Control.ForegroundProperty}" Mode="UpdateTarget" />
    </i:Interaction.Behaviors>
</Label>

Dependencies

Note that http://schemas.microsoft.com/expression/2010/interactivity namespace is available under a NuGet package called System.Windows.Interactivity.WPF. It will also be automatically added if you open the project in blend.

Copy and paste code

using System;
using System.Threading;
using System.Threading.Tasks;
using System.Windows;
using System.Windows.Data;
using System.Windows.Interactivity;

namespace Lloyd.Shared.Behaviors
{
    public class PeriodicBindingUpdateBehavior : Behavior<DependencyObject>
    {
        public TimeSpan Interval { get; set; }
        public DependencyProperty Property { get; set; }
        public PeriodicBindingUpdateMode Mode { get; set; } = PeriodicBindingUpdateMode.UpdateTarget;
        private WeakTimer timer;
        private TimerCallback timerCallback;
        protected override void OnAttached()
        {
            if (Interval == null) throw new ArgumentNullException(nameof(Interval));
            if (Property == null) throw new ArgumentNullException(nameof(Property));
            //Save a reference to the callback of the timer so this object will keep the timer alive but not vice versa.
            timerCallback = s =>
            {
                try
                {
                    switch (Mode)
                    {
                        case PeriodicBindingUpdateMode.UpdateTarget:
                            Dispatcher.Invoke(() => BindingOperations.GetBindingExpression(AssociatedObject, Property)?.UpdateTarget());
                            break;
                        case PeriodicBindingUpdateMode.UpdateSource:
                            Dispatcher.Invoke(() => BindingOperations.GetBindingExpression(AssociatedObject, Property)?.UpdateSource());
                            break;
                    }
                }
                catch (TaskCanceledException) { }//This exception will be thrown when application is shutting down.
            };
            timer = new WeakTimer(timerCallback, null, Interval, Interval);

            base.OnAttached();
        }

        protected override void OnDetaching()
        {
            timer.Dispose();
            timerCallback = null;
            base.OnDetaching();
        }
    }

    public enum PeriodicBindingUpdateMode
    {
        UpdateTarget, UpdateSource
    }

    /// <summary>
    /// Wraps up a <see cref="System.Threading.Timer"/> with only a <see cref="WeakReference"/> to the callback so that the timer does not prevent GC from collecting the object that uses this timer.
    /// Your object must hold a reference to the callback passed into this timer.
    /// </summary>
    public class WeakTimer : IDisposable
    {
        private Timer timer;
        private WeakReference<TimerCallback> weakCallback;
        public WeakTimer(TimerCallback callback)
        {
            timer = new Timer(OnTimerCallback);
            weakCallback = new WeakReference<TimerCallback>(callback);
        }

        public WeakTimer(TimerCallback callback, object state, int dueTime, int period)
        {
            timer = new Timer(OnTimerCallback, state, dueTime, period);
            weakCallback = new WeakReference<TimerCallback>(callback);
        }

        public WeakTimer(TimerCallback callback, object state, TimeSpan dueTime, TimeSpan period)
        {
            timer = new Timer(OnTimerCallback, state, dueTime, period);
            weakCallback = new WeakReference<TimerCallback>(callback);
        }

        public WeakTimer(TimerCallback callback, object state, uint dueTime, uint period)
        {
            timer = new Timer(OnTimerCallback, state, dueTime, period);
            weakCallback = new WeakReference<TimerCallback>(callback);
        }

        public WeakTimer(TimerCallback callback, object state, long dueTime, long period)
        {
            timer = new Timer(OnTimerCallback, state, dueTime, period);
            weakCallback = new WeakReference<TimerCallback>(callback);
        }

        private void OnTimerCallback(object state)
        {
            if (weakCallback.TryGetTarget(out TimerCallback callback))
                callback(state); 
            else
                timer.Dispose();
        }

        public bool Change(int dueTime, int period)
        {
            return timer.Change(dueTime, period);
        }
        public bool Change(TimeSpan dueTime, TimeSpan period)
        {
            return timer.Change(dueTime, period);
        }

        public bool Change(uint dueTime, uint period)
        {
            return timer.Change(dueTime, period);
        }

        public bool Change(long dueTime, long period)
        {
            return timer.Change(dueTime, period);
        }

        public bool Dispose(WaitHandle notifyObject)
        {
            return timer.Dispose(notifyObject);
        }
        public void Dispose()
        {
            timer.Dispose();
        }
    }
}