9'er...
That Pico thing ain't much of a PLC. It is a "switcher".
However, if you are willing to use a real control relay in addition to the light, this will do you.
The switch at the left is the primary source. The Normally Closed CR Contact is of course controlled by the Control Relay.
The output from the top timer goes to the light AND to the input for the bottom timer. These are real inputs and outputs.
When the switch is closed, CR is OFF and -|/|- is closed.
The top timer runs for 1-second then turns ON the light.
When the light comes ON, the bottom timer runs for 1-second.
When the bottom timer times out, the CR is turned ON which opens the contact... the top timer is reset along with the bottom timer.
The -|/|- closes again and the cycle repeats.
This shouldn't be too tough on the CR Contact. However, the same effect can be had with a solid-state switch without stress.