Hi,

I agree with Dave Steven’s assessment of an ignition system weakness or battery input voltage may be dropping out or down during cranking.
The ECU and ICU systems use very small and specific voltage signals and frequency waves to respond too.

How old is the battery?
Another question is has the battery ever set for a long time without a routine of being used.
Allowing a battery to sit too much drains years of service life away.
A float charger can help to reduce the sulfating plates in lead acid batteries.
In a week to ten days of non-use starts a downward life cycle.
In other new age batteries it’s darn dendrites!

The CPS is not something to dismiss lightly either.
Hard starting or idling rough and slow or a streak of light miss fires that seem like a rich or lean mixture can be from ill timing that is starting with the CPS.
They do degrade slowly and any frayed insulation is a definite heads up.
I pulled one coated with an oily grime. Inside it there was softened signal wire insulation.
Well below the shielding that doesn’t seal a thing.
Until you actually handle it and wipe it, it looked intact.
If it’s original get rid of it or even if it’s the second or third one (?) that helped put 295,000 on my 1991.

There is another middleman in all of this that gets ignored and it’s because it’s behind the battery.
The item is a spark relay the switches the ignition coil on and off causing it to work.
This item works when it gets signals from the ICU, that the CPS talks too. It’s a chain of events that takes a second or so to get going. And that’s when everything is nice and right on.

If you get to it, Unplugging helps sometimes by exercising the pins surfaces and apply dielectric paste.
Check the pins for corrosion.
If you have time, put fresh heat sink paste between the base and the transistor for summertime driving.
About every ten years under terrible environments keeps it happy.
I had one go bad that it shut down the engine real regularly like in 30 seconds after starting.
Your right, having a few spare parts cars available is my Cheshire Cat Smile! 😏

The ICU has to tell the ECU to turn on the injectors and fuel pumps, through a system relay, that also powers up the AMM.
Hesitation along any of those items above, extends the cranking times.
So, you have to follow a path of one orange wire in a schematic to see the circling of both systems.
The CPS, is the guy who yells out “the engine is moving now” and then the chain wiggles to tightens up everything to turn on!

It’s like you are in a dark closet and you know there’s a light bulb in the middle.
You just need to look or more likely “feel” around to make the chain links tight, of which, will come from knowing how it works. 😊

Good luck this weekend!

Phil