Step 16 : Circuit Modification Option 5

Not as good as option 2 but neater than option 3. Install a nicad or NMHi battery so the battery gets trickle charged while the mains power is on then runs the IC when the power is off.
When the power is on the battery trickle charges via the 1k resistor (about 5mA). When the power is off the battery runs the chip.
A good source of batteries is old mobile phone batteries. The sort that were about 4 inches long by 2 inches wide. Disposal stores here sell new ones for about $1. They contain 7 very thin 1.2v NMHi batteries inside. Break them open by hitting them gently on the edge with a hammer.
The battery may fit entirely inside the case but usually doesn't. If not just run the wires to the outside and tape it to the case.
The only drawback with this option is that at the start of the season the battery will be drained. When you turn it on the battery draws all incoming power and the lights don't come on. Just be patient. After about 5 minutes it will all work. Leave it on all day to charge up the battery. If not, try changing the 1k resistor to a 2.2k.
You could remove the battery and charge with an external charger but that defeats the whole purpose of this option which is to be able to tape it all up and leave it. If you do that you might as well use option 3.