question

The CCGX only has an simple inbuilt relay that is CLOSED when the generator is intented to start and remain running. The relay then OPENS when the generator should stop.

So with this in mind you really need to look at what your generator control unit requires to see if the CCGX relay can be directly connected or if some additional wiring or equipment is required.

The information provided in your question about the generator control unit logic is not really enough to help any further.

use a magnum me-ags-s. It's a standalone AGS system with 3 relays inside, with many different timings and modes so that it works with almost any generator. You can also use it to set additional run conditions.

See the following accessories:

The following two Pigtail Adapters are available from Magnum Energy for
use with the ME-AGS-S. They are useful in applications where there is a
requirement to conveniently and automatically turn the generator on/off
externally through a manually controlled switch or from an automatically
controlled switching device (i.e., use air conditioner thermostat controls to
turn gen on to run air conditioner):
The ME-PT1 (Pigtail One-wire) adapter is designed to allow the AGS to start
the connected generator when an external +12 volt DC supply is applied.
The ME-PT2 (Pigtail Two-wire) adapter is designed to allow the AGS to start
the connected generator by an external two-contact switch

You'll want the ME-PT2, wire it to the NO and COM of the Victron generator relay. Then the ME-AGS will control the generator as long as you have its other run conditions met.