You're on the right track.

In your service initialization code:
- Create a System.Timers.Timer object
- Set the Interval (perhaps to 1000, to check the current time once every
second, or 10,000 to check every minute)
- Attach to the timer's Elapsed event
- Enable the timer

When the Elapsed event fires:
- check the system time
- if the system time is the time of day you are waiting for, run the other
app; otherwise do nothing

You will probably want to keep a flag that indicates the last day the
program was run, and when you are checking the current system time, see if
it is not only on, but also possibly past, the time you want to run your
other program, and also check the last-run flag to make sure it is not
today. This way you won't miss a day if the system gets busy and the timer
doesn't have the opportunity to fire on the exact second or minute you're
watching for.