If I'm tapping into a wire I strip back about 1/2" of insulation wrap the "new" wire into the existing wire , Solder connection then wrap with electrical tape ...
If I'm adding extra circuits I strip back the existing wire then add the additional wires then use crimp caps then tape over the crinp caps
Crimp caps are shaped like wire nuts , but the tops instead of twisting you use a wire crimper on ...
I use Heatshrink tubing instead of elecrtical tape