Depending on the search index, you may need to include the web.config key to accept all SSL Cert errors.
<add key="CMSSearchCrawlerAcceptAllCertificates" value="true" />
By default, the smart search crawler does not index pages on sites using a secured protocol (HTTPS) without a certificate from a trusted authority. For example, you may encounter the problem in development environments that use a self-signed certificate.
If you set this key to true, the system accepts all certificates.
Note: Setting the CMSSearchCrawlerAcceptAllCertificates key to true poses a security vulnerability and should not be used in production environments.
Also, what is the specific 500 error? Have you checked the servers event logs and really dug into the error? If your server is in a DMZ or load balanced there could be other firewall issues restricting it.