Hi @Don Price , thank you for posting in the Q&A forum.
The Page Layout (Welcome Page) Search People is only available in the site template Enterprise Search Center in SharePoint Sever 2016.
The People Search Core Results web part is not available to be manually added via Web Part Categories either.
Please navigate to the Enterprise Search Center in your farm (create it first if you do not have one yet), go to Settings > Site settings > Page layouts and site templates and then add (Welcome Page) Search People to "Pages in this site can only use the following layouts" list under Page Layouts.
After that, you can navigate to the Pages Library and create a page using this template.
Here is a related post on creating employee directory in case you need it: How to: Create a Simple SharePoint 2013 People Directory.
*Note: Microsoft is providing this information as a convenience to you. The sites are not controlled by Microsoft. Microsoft cannot make any representations regarding the quality, safety, or suitability of any software or information found there. Please make sure that you completely understand the risk before retrieving any suggestions from the above link. *
If an Answer is helpful, please click "Accept Answer" and upvote it.
**Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread. **