Some times ago, I got some cheap Christmas garland LED light power by 2 AA batteries.
I wanted to put them outside, with no AA battery and recharge by the sun.
For the blinking part, I used a simple uC from Microchip, 12LF1572.
A simple button will move with different sequences of blinking, including one with random timer (default one).
As there is a solar call for recharge the LiPo battery (through a Schottky diode) , a simple trimmer connected to the solar cell will be use to detect day and night  status.
To limit the consumption of the battery, a timer which is 6h by default will make the garland blink. However, this timer can be change by pressing the button at switch on, from 6h to 12h (the leds will blink to the number of hours).
The software is written in C under MikroC. Some improvements still can be done like to save some parameters in the flash. 
For the casing, thanks to Louis who made this casing, simulating 2 AA battery (under thinkercad). 
On one side of the casing there is the LiPo battery (here a 180mAh) and the small PCB on the other side.

Louis and Laurent Labbe