If you'd like to create qualifying questions that determine whether or not you collect contact info or even more follow-up questions on a different page, like scheduling, to respondents that give the right answers you define, then Qualifying Question is a question type that might be helpful.
Here's the outline on how to use it, and the most common/awesome scenario is to use qualifying questions as a guardian gate in front of your scheduling question, so only the right participants get to choose a time. Added bonus is that you can only ask for PII (Personally Identifiable Information) from respondents that are qualified. The big advantage over the Magic Drill Down question type is that with qualifying questions you can have multiple separate questions across multiple questions pages in your screener.
Step 1: Choose Multi-Page Theme
Use the campaign theme from screeners >> design >> theme. Currently, this is the only theme that supports qualifying questions.
Step 2: Add Qualifying Question(s)
Add one or more questions that will determine if your respondent is allowed to pick a time. They are additive so all correct answers to multiple qualifying questions will be required to see the next page.
Step 3: Add Second Page
Add a second page to your screener so you can put scheduling, contact fields, or whatever you'd like to only show to the right respondents, on this page. You simply drag questions from one page to the next. It's a bit clunky, so apologies, but you might have to reload the page to make sure everything worked right. Working on fixing that, obvs.
Step 4: Optionally Show Disqualified Page
Don't tell people explicitly they are disqualified, because then you increase the odds they will get angry and email your customer support, but you can offer different wording than if they were qualified. Let's call it a more gentle thanks.
The only other important note is you can get pretty creative with page skip logic, so your MPS questions don't have to be on the first questions page. There's almost infinite ways you could combine with drill downs as well. Give us a shout with any questions.