Firstly, that link takes the forum poster to the custom form from Wix, which is provided by Wix Forms.
If you want complete control and to make up your own lightbox, then use the Corvid method out of the three options.
https://support.wix.com/en/article/about-the-member-signup-form#corvid-form
Plus, if you do your own lightbox, you will need to change the signup settings to suit too.
https://support.wix.com/en/article/corvid-enabling-custom-site-registration
See here for previous post with example code and links for more help on it.
https://www.wix.com/corvid/forum/community-discussion/custom-member-signup
Wix also do an example to about it.
https://support.wix.com/en/article/corvid-tutorial-creating-a-custom-registration-form-with-code
As for the Google only signup, well as you asked for Google, see here,
https://www.wix.com/corvid/forum/community-discussion/solution-google-facebook-user-information-on-login