I got 15min out of this rule... Of course you need something else to trigger it because it blinked off and immediately turned on again. The attachment shows the THEN portion.
IF Link1 (a GE Link bulb) is OFF THEN Link1 ON, delay 300 seconds Link1 ON, delay 300 seconds Link1 ON, delay 300 seconds, Link 1 OFF
Obviously you would want something more like:
IF Link1 is OFF AND Button1 is ON THEN...
It may be a workaround, but it did work.