Here’s an idea for an Xmas themed project, using up a few components most people are likely to have floating around. At the heart of it is a 555 timer, which creates a regular “pulse”.
We’re using this on/off behaviour to drive two transistors – one NPN and one PNP

Xmas Tree Sch

When the 555 timer output goes high, the NPN transistor allows current to flow lighting up LEDs 1-4. At hte same time, the PNP blocks current and LEDs 5-8 go out. When the output goes low, the NPN stops the current flow, making LEDs 1-4 go out, while the PNP makes LEDs 5.8 light up.

Play about with the values of the two resistors, R1+R2, between pins 6+7 on the 555 timer, and the value of the capacitor to create different flashing frequencies.

The 555 timer can sink/source up to 200mA. As this is an untested design, and depending on the voltage of the battery used, a resistor between power and the common LED anodes may be required. The value of this resistor will depend on the power source used

Xmas Tree Pcb

Create two of these PCBs. Cut a slot from the top of the first board, to about the mid-point, and from the bottom to the same point on the second board. The common power supply to the LEDs makes a complete circuit around the outside of the board, so it shouldn’t matter if it’s cut at the top or the bottom (just not both!)

On the first board only, mount the 555 timer and associated discrete components. On the second board, simply populate with LEDs.

Slot the two boards together. Every LED has two holes alongside it. These are for connecting wires to the corresponding hole(s) on the other board. This creates a complete circuit between all the LEDs.
Don’t use straight bits of bare wire – use coloured wire (coloured sleeves) and bend them slightly to make “loops” going across the branches. For a real Xmas feeling, cover in glitter or bits of tinsel.

Connect up a battery and see if it works.
(this design, at the time of writing, is untested!)
Here’s the silkscreen/layout: