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It depends on what you mean by "observed" - do you mean direct observation in real-time or something that can be seen indirectly as in the fossil layer or say a videotape? I think the first is overly restrictive - and you've stipulated the second so I'm still not sure where you're going with this.

The first isn't overly restrictive, it's the normal means by which we confirm scientific theories. A theory of Evolution dependent on random spontaneous mutagenic speciation predicts that we will see the random spontaneous mutagenesis of species. So far, we haven't.
So, random spontaneous mutagenic speciation remains unconfirmed by direct observation. The absence of obesrvation doesn't disprove this possible mechanism for evolutionary speciation, but it prevents us from presuming it to be true.
In the second case, you misunderstood what I stipulated... I believe the fossil record indicates evolutionary speciation. I believe it is utterly silent as to the cause of that speciation. It informs us neither about random causes, nor about Intelligent Design, nor about the Dr. Seuss, nor about any other theory.
What that means is that appeals to the fossil record have no bearing on what the causes of evolutionary speciation actually are.
So... where is the evidence to support the contention that random causation explains evolutionary speciation?
In direct observation? No. In the fossil record? No.
In the absence of such evidence, don't we have to allow for the possibility of some non-random cause of evolutionary speciation?
Where I'm going, head-on since post #1, is at the intellectually dishonest, unscientific adherence to the notion of random causation of speciation, to the exclusion of non-random theories.

In the absence of such evidence, don't we have to allow for the possibility of some non-random cause of evolutionary speciation?

Do we have to allow for the possibility? Sure. Do we have a felt need to bankroll it or teach it in school? Not obviously. Natural causes has turned out the be a satisfactory explanation for things we didn't previously know every time the question has been put to the test so far. Let's not be making stupid bets out of a sense of fairness.

The first isn't overly restrictive, it's the normal means by which we confirm scientific theories.

No it isn't. Many sciences rely on indirect evidence. Our visual system is fairly restrictive in terms of what it can resolve so we quite often rely on indirect evidence for things that are too small, too large, or take too much time to witness in a lab. Many other things we simulate and look for good evidence that our simulations actually reflect reality.