I had no problems when I signed up from my old computer (using firefox), immediately saw a "snipe it" link added to all eBay pages. But from my new computer (switched to Safari), there are no snipe links for me on eBay. How do I get the link to show / initiate a snipe?

This "snipe it" plugin is for Firefox so it will not work in other browsers.
If you want to see it on your new computer, you have to install Firefox and add-on:
http://www.firefox.com/
https://addons.mozilla.org/en-US/firefox/addons/policy/0/5571/34447