Develop a custom timer (firmware and circuit schematic) based on PIC microcontroler (preferably PIC16F88I/P) providing 3 min, 9 min and15 min time periods (switch selectable) running in continually (cyclic ON- OFF), push button resettable and driving one latching relay (such as OMRON G6K or similar).
Device has to be power by 9V battery and be energy efficient to maximize battery life. No PCB needed it will be done by the time of enclosure design.
I guest that you are looking for an industial product. I can help you in your project. If you prefer me, I can upgrade your circuit according to your needs.
Have a nice day.