Battery backup was not understood from #1 , rather we assumed to be switched ignition. A large Coin Cells has an ESR of ~~1k .
CD4017 will draw < 20uA from 3V coin cell. This can be reduced to near zero with 10V drop/20uA or 500K pullup to 12V.
Depending on colour and Vf, 2~3V for Red to Blue/Wh the LED drain can be switched low with ~9V +/-? Zener diode to V+ (an no inverting driver driver. This dim Led can also serve as Battery voltage meter as CD4017 is around 200~300 Ω using 10~15V.
But for consistent high brightness, ULN2002 inverting buffer is more reliable. ONLY 1 pullup R is needed between switched V_+and LED Common Anodes, since only one LED is on a time. Depending on CD range of LED choose 5 ~20mA for desired brightness from Ohm's law for V drop) e.g. 12Vbat -3V(white)-1V (Darlington@10mA) = 8V so for 10mA choose 760 Ω or for 16 mA choose 470 Ω.
Each R and C in my schematic has dual purposes for filtering and timing, but not critical in tolerances. Adjust on Falstad Simulator and test to verify
Changing the input 100R to 1000R will delay switching to 100us ( with 100nF) and reduce load dump current to CD4017 which has input diode clamps to V+/gnd from ACU inductive clutch (K.I.S.S. has shown correct automotive requirements)
If any CMOS gets a pulse that pulls internal diodes more than 1V above Vcc even for a 10 nanosec or below gnd by same, then CMOS chip turns into a TRIAC across battery (CMOS latchup effect) and gets hot until power is removed or fries depending on ESR.
As you see there is more to a reliable design than what appears on the schematic.