Tiny RTC as simple relay timer.

I have a Tiny RTC, this model to be exact: http://www.ebay.com/itm/Arduino-I2C-RTC-DS1307-AT24C32-Real-Time-Clock-Module-For-AVR-ARM-PIC-SMD-/170910326110?pt=LH_DefaultDomain_0&hash=item27cb0c9d5e

I was curious if I could set it up to run a simple switch based on time, independent of the arduino. Any thoughts?

The DS1307 (http://datasheets.maximintegrated.com/en/ds/DS1307.pdf) doesn't have an alarm feature so you can't program it to turn a load on or off at a specified time. I think you need two alarms and a Set/Reset flipflop (or latching relay) to get what you want.

Look for the DS1375 or DS1337 (or the DS1337C which includes the crystal