First the basics of curl:

Curl Manual https://curl.haxx.se/docs/manpage.html

curl https://my-site-under-test.com -v -o /dev/null

This will use the HTTPS protocol and print out verbose info. It will discard the HTML body to "/dev/null". You can remove -o and the "/dev/null" if you need to see the HTML or other returned content, i.e. you need to confirm the web page is returned.

Curl with Sauce Connect Proxy 

curl --proxy localhost:3788 https://my-site-under-test.com -v -o /dev/null 

1. Start a Sauce Connect tunnel or find the logs of an existing tunnel.
2. Obtain the port used by SC from the logs. Looks like: Started scproxy on port 52178
3. curl -I --proxy localhost:52178 www.google.com

Curl with a generic proxy (not sauce connect)

curl --proxy username:password@proxy.com:port https://some-website.com -v

Can the host machine hit the RDC Tunnel API?

curl --user RDC_USERNAME:RDC_ACCESS_KEY https://us1.api.testobject.com/sc/rest/v1/RDC_USERNAME/tunnels -v -L -X GET

If you can curl a destination, say a site under test, and get a response, then Sauce Connect should be able to get there too.  So before delving into Sauce Connect verify all the basic network connections exist via curl.

1. curl the site under test
2. If it fails check for a proxy.  curl with aforementioned proxy, see "Curl with a generic proxy"
3. Start sc and curl with sauce connect. verify the curl from step 1 and step 3 match.