It's a curious question and the answer may be good or bad depending on your perspective. "Why doesn't FileMaker have a time picker?". It has a calendar widget for working with date fields, why not time values?
The solution to the problem, as is often the case, can be managed by simply creating your own picker. In fact, if you don't like FileMaker's desktop based date picker you can create any variation you desire based on being able to create any style of layout you can imagine. While the same applies to a time picker, it may not be obvious how to implement if you've not worked with FileMaker for some extended amount of time.
In this video, I showcase a straight-forward time picker which works with both timestamp fields and time fields. It also includes some valuable utility scripts and concepts which can certainly be used in other areas of your FileMaker solutions. If you've ever come across the need for a time specific picker then adding this to your solution should save you a ton of time!
Click the title or link to this article to view the video.