Ask the video owner to share the private video with your Google account email
Sign in to YouTube with the exact Google account that was granted access
Open the private video link from the invitation or shared URL
Make sure you are using the same account on the device and browser
Check your email for the sharing invitation from YouTube
Accept the invitation if prompted
If the video still does not play, confirm the owner has not removed your access
If needed, ask the owner to resend the invitation to the correct email address