I'll have a go.
My guess is Ineos left the red wire off for the Smartpass (as Ctek likely advised them to) because Ineos & Ctek expect owners with the service battery optioned to fit a Ctek 250SE (which Ctek recommend & Ineos left space for), they assumed we'd all likely be running a fridge etc. This leaves the SP (Smartpass) as a 'dumb' bulk charger and slave to whatever voltage the alternator produces so it'd only be effective when the 105Ah service battery was heavily depleted, which is when you really want it to kick in and boost the 'bulk' charge rate. This is because the service battery's SOC (state of charge) rises as the resistance (& temperature) in the battery rises, the SP then starts to throttle back and eventually drop out completely I suspect, maybe to only a only few amps. This likely happens around 20A charge rate which is where the 20A rated 250SE takes over to finish the job as it *can* regulate the alternators supply voltage to suit the service battery's rising internal resistance & temp. I'd say the 250SE red wire should be connected as per the Ctek manual, no harm in trying and seeing with a clamp meter what's happening with and without the red wire. And it might tell you more about how the vehicle's ECU/BCM is communicating with the setup, if at all.
No real point in connecting the SP's red wire (but you could also maybe try that) as you only need it to assist with bulk charging - the 250SE and say 5A from the SP is typically enough to recharge the service battery after losing say 20-30Ah overnight to the fridge etc. If the service battery is down at say 40-50% SOC (likely most nights) the Smartpass will ramp up and do the heavy lifting until internal resistance & temperature causes it to wind back, this would get the bulk of charge into the battery and from there the 250SE's 20A finishes the job, especially with such a small service battery, 105Ah is a borderline size to run a 40L fridge without solar to assist (more reasons the 250SE is a must fit). I think the Smartpass has primarily been used as a good solution to bridge the batteries, maintain the starter, provide Start Assist - and isolate the loads (fridge etc) by utilising the alternator while on the move allowing the 250SE to operate effectively as a multi-stage charger without interruption - not so much the SP's ability to charge at the 120A especially in this scenario with an small EFB batt (definitely a benefit with a lithium setup though). A simple VSR & 250SE just wouldn't cut it.
If you replaced the EFB service battery with a lithium you don't have the resisitance (or temperature) issues so I'd then likely connect the Smartpass's red wire so you get the full benefit of maximum charge from both units. A 100-200Ah lithium will accept everything you throw at it right up to about 95% SOC so you might see 100A or even more going in depending on the battery's mgmt system (BMS). You'd only need less than an hour of engine time to replenish the service battery.