For me the CH recommended foundations for a relationship with a bound spirit companion: respect, friendship & admiration hold true equally for one that is an immortal.
If you have a CH RA Immortal binding of Zeus (ie if it was originally conjured and bound by CH and not another seller), they have essentially 'negotiated' the agreement with that god to be a lifelong companion for you as a bound spirit. I mean that is the way the conjuring and binding will have been done, in my way of looking at it.
So you're not starting with a blank slate. Zeus has already agreed to this companion binding.
I have probably half a dozen immortal bindings, 2 of which are Greek. I treat them as part of my spirit family but keep to the CH offerings, suggestions etc. By that I mean I don't bring in practices from outside of spirit keeping. I do have the Immortal commune offering & stone that CH sells and offer that too.
see also
https://www.creepyhollows.com/faq/index ... light=zeus
As a side note, I've worked with the Greek deities for a long time using a non-spirit keeping system, a form of mind magic, in which the deities' energy fields and personalities etc are contacted non-ceremonially. Ceremonial deity interaction isn't the only way to go.
But respect definitely is...just as with all of our bound spirit companions.
I think deities have got used to being treated as gods / immortals and the special respect that goes with that, so maintaining that attitude makes sense. I have an Indian deity binding and use a well known mantra for that one and their title in Sanskrit, just to connect (not as a spiritual practice with them), as I think they respond well to that.
One thing I do is to compartmentalise the different spiritual systems I work with. So I interact with a CH Greek immortal binding as I would with a CH spirit companion and, when I work with the same Greek deity using the mind magic system, I relate to it/them entirely that way. I don't mix the two.
It makes sense to me to do this but I realise other people will have a mix of different approaches from me.