Decisions are an art, not a science. There is no right or wrong answer. Rather, it's a judgement call based on what you know. I take multiple decisions with limited information as a software product maintenance leader.

Step 1 - What is known

How small and ignorable it is.

For example, in the case of a customer problem that is not progressing, your customers will conclude you are not progressing. Let them know what has been ruled out based on what you know. I think that's a good start.  

Step 2 - Compile trends

If available, evaluate data points from similar decisions. Success in the previous instance may not repeat, but its chances are higher.

Step 3 - Find your community and get help

"Ask five different people what's going on in orbit...and you'll probably get ten different answers."  Alternate viewpoints spark discussions.

Decision Time - Moment of truth

After gathering all available information, apply the Pareto principle. Which 20% criteria's influence 80% of decisions? You will have one or two major points that will help you make your final decision.

Final lesson - One-Way and Two-Way Doors

To optimize for decision quality or speed, consider decisions as either one-way or two-way doors. A two-way door can be easily reversed if you're wrong, so prioritize decision speed. A one-way door is rarer. You cannot reverse these decisions easily, so gather more information if you are unsure.

You'll be surprised to realise that most of your decisions are two-way-door, so speed trumps perfection.