If you are familiar with CMOS, it would help
https://www.fairchildsemi.com/datasheets/CD/CD4060BC.pdf
This old chip has an RC oscillator type built in with a 14 stage binary counter , which means you can use an external or the internal clock set by a RC values to anything you want and use AND OR Gates to combine outputs to create a delayed pulse after With multiple pulses.
https://www.elprocus.com/5-different-timer-circuits/
There is also the CD4017 decade counter which allows you use any clock like a 1 Hz clock then sequence events for 1 second at a time with 10 outputs going high sequentially.
A Google "Images" search for CD 4017 schematics will give you some ideas.
The variable frequency clock or VCO would be the next improvement if you are up to this so far.
This can be done as suggested already with a voltage controlled one-shot.. Just someone needs the time to put it all together for you...
There are some extra details you need to define.
Power up by detecting engine start? or just ignition power
Slow ramp ? or just as is with fast start and quick stop?
Does Tach get disabled ? or does it revert to normal operation?