Several connectors have a switch to use Net::SSL instead of the default IO::Socket::SSL class.
The SSL backend is set only on first load of the appropriate class, so a second connector instance with other settings inherits the wrong setting causing the connector not to work if options are used that are mutually exclusive.
Possible Solution: Init code in Net::HTTPS internally uses module variable SSL_SOCKET_CLASS to manage the backend. Might help to directly set/reset this.