To answer your question:
Since your other Gmail account was able to receive your test email, it means and we can conclude that this additional email is working just fine.
Since you have not received any FDN (Failure Delivery Notification), it also means that your test email was delivered and the ball now is on the receiving party. If the recipient's email server rejects the email from your additional Gmail account, you will also be notified indicating failure of delivery due to the recipient's email rejected your message.
Since you did not receive such notifications, few things happen here.
The receiving email could have delivered your email directly to the Junk or Spam folder. Please contact that other person whom you sent the test email and ask him/her to check his/her Junk or Spam folder. If your test email is there, please ask her to mark the email Not Junk or Not Spam so that your future emails to him will be delivered to your Inbox.
If he cannot find your email in the Junk or Spam folder, please give about 24 hours and see if you will receive and FDN, or he gets your test email.
Another unlikely thing to also happen is, your email could have been blocked by the recipient. I said unlikely because, if this email is not used regularly, then there is no way he could have blocked it.
I am still waiting for you to join me in the remote session.