Asking what they tried before is the question that gets me the most useful answer. Before a call I also check what tools the company already runs on their site, so I am not asking things I could have looked up. I built https://stackshortlist.dev partly for that.
StackShortlist
Proof Over Promises.
"What happened that made this important now?" is the question that does most of the work for me too. The answer usually tells you both the real problem and whether there's an actual deadline behind it. Do you also ask who tried to fix it last time? I've found that tells you a lot about internal politics before you scope anything.