Sharepoint 2010 Foundation - changed to https, seach stopped working

We have a small Sharepoint 2010 Foundation installation with an application server and separate SQL server.

For compliance reasons, we need to make our Sharepoint site https.  The site was originally configured for http.

We set an HTTP redirect in IIS to use https and the site works fine with no issues.

However, after stopping the http site in IIS, the Sharepoint Foundation Search v4 no longer shows any results.

In Event Viewer, there are errors that the crawler cannot access the database sts4://

I'm assuming this needs to be changed to sts4s:// somehow.

I have tried creating alternate access mappings using https but the event viewer floods with errors trying to access http.
Event 8059 (SharePoint Foundation) of severity 'Warning' occurred 106 more time(s) and was suppressed in the event log

Is there an easy way to get the Foundation Search working over https?  I do not see anywhere else to configure the paths for the search.  Also, we are not Sharepoint developers and the person who setup the site is no longer with us.