A blinking light from these timers usually indicates the neutral is not properly wired to the switch. Exactly how did you wire this switch?
I also have the 15071 and found the same problem. I have a very complicated box I'm trying to wire into that has four switches. Two of which, to my knowledge, don't do anything. The rocker switch I am replacing controlled our front porch light. When I wire it as the previous switch was wired, I get this same result of the light turning off when I turn it on. All the white wires in the box are bound together with a wire nut. When I wire the white wire from the switch into this grouping the light doesn't turn on at all.