Создайте такой класс:

using System;
using System.Timers;
using System.IO;

public class Example
{
   private static System.Timers.Timer aTimer;
   
   public static void Initialize()
   {
        // Create a timer with 10 minutes interval.
        aTimer = new System.Timers.Timer(10*60*1000);
        // Hook up the Elapsed event for the timer. 
        aTimer.Elapsed += OnTimedEvent;
        aTimer.AutoReset = true;
        aTimer.Enabled = true;
    }

    public static void OnTimedEvent(Object source, ElapsedEventArgs e)
    {
        // Write system time to log file
        using (StreamWriter sw = new StreamWriter("log.txt",true))
        {                
            sw.WriteLine(DateTime.Now.ToString());                
        }
    }
}

при запуске программы (или службы) вызовите метод Initialize