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Given the premise that deductive reasoning needs a premise statement to get started, ultimately do these premises come from inductive observation? e.g.
When the sun is out it’s daytime. The sun is out. Therefore it’s daytime.
This implies that some observation has concluded the premise of the sun being out, and having some sort of correlation to some pattern of the sun coming out?
I don't think that axioms like 'A thing cannot have both a quality and its opposite' can be acquired from observation.
Nobody can show us what 'not' means. The opposite of red is not brown, or blue, or something else we can actually encounter. But we believe right off that there are red things, and there are things that are not red. There is a logical jump we have to make for ourselves.
The idea that things have opposites comes naturally, to the extent that we somehow expect things to have opposites that just can't have them. (I have recently been asked, "What is the opposite of a barrister?")
So, not all deduction can be based on observation. Some of it is in the nature of language, at a level that seems inborn, but is at least tacit and involves necessary, predicted generalizations beyond observation that we are all expected to make in the same way.
Does all deductive knowledge stem from inductive observation?
Strictly speaking, there is no "deductive knowledge" and there is no "inductive observation". There is only knowledge, observations, and beliefs. However, what most people would call knowledge is actually beliefs. They would say they know they have a tree in their garden when in fact they only believe that. This is also why our theories are revisable. If we knew our theories true, we could never revise them without producing a false theories instead.
Deductive logic is all we need in a world about which we know nothing, not even that there is one. We only need deductive logic because we are capable of living our lives on the sole basis of our beliefs about the world. We trust our senses. People who don't starve to death and don't reproduce and their genes are selected out. People may be dogmatic about things like God and what not, but they are all prepared to revise some of their beliefs whenever their senses make them feel the pain of their mistakes.
To express this in your quirky terminology, inductive knowledge follows from inductive observations, and this is all we need to survive in our world.
What about knowledge itself? Well, clearly, there are things we know. I know I have the impression of seeing a tree in my garden. From this, I will derive the belief that there is a tree in my garden.
So, essentially, we know what we know, and logic never gets to be used to infer any knowledge which is not already apparent in the premise. So, if the premise is that I know I have the impression of seeing a tree in my garden, then all I can infer is that I have the impression of seeing a tree in my garden.
There's no inductive observation, all observations by definition are empirical through senses (instruments can be classified as our extended senses). I think you're asking about whether deductive reasoning necessarily entails inductive reasoning. These two are completely different modes of reasoning. A deductive reasoning system whose axioms/assumptions/premises (most powerful enough deductive systems need) may not be required to be observed actually true, one can always introduce an unverifiable premise like "It's necessary that if a thing exists then necessarily so" as just recently discussed in a previous PSE question here. Or in math most of us implicitly use ZFC set theory as a foundational deductive system, while the famous C part (Axiom of choice) cannot be observed to be actually true from any experience since it's really about choice from infinitely many sets each of which having no choice function and many mathematicians doubt its soundness and try to avoid using it. Also recently in physics one can express physical laws in terms of impossible or counterfactual/possible modes which goes beyond traditional empirical observations of only what's actual, such as David Deutsch's Constructor theory.
