Hello,
We’re sorry to hear that you’re experiencing a 500 error when trying to connect Google Analytics without the service account. The 500 error typically indicates a server-side issue.
To resolve this, please ensure that your server is properly configured to handle the connection with Google Analytics. Additionally, you may want to check if there are any server logs or error messages that could provide more insight into the cause of the 500 error.
If the issue persists after checking these settings, please reconnect your Google account as shown in the following screenshot:

If the issue persists even after you reconnect your Google account or you see a red signal again when you validate your connection, we would suggest you open a support ticket here and share the error log with us.
If you have any further questions or need assistance, please feel free to reach out to our support team directly from here, and our support expert will be more than happy to help you out.
Sources:
Resolving Rank Math Analytics Related Issues » Rank Math
Google URL Inspection API Integration in Rank Math
How to Fix PCLZIP_ERR_BAD_FORMAT (-10): Unable to find End of Central Dir Record signature » Rank Math
I do not have “Reconect” button
Hello,
Please make sure that you are using the latest version of our plugin: https://rankmath.com/changelog/
If the issue persists, please share a screenshot of the error you are getting and the Analytics settings in WP Dashboard > Rank Math SEO > General Settings > Analytics. You can use a tool like https://imgur.com/ to share the screenshots.
Looking forward to helping you.
Hello,
Since we did not hear back from you for 15 days, we are assuming that you found the solution. We are closing this support ticket.
If you still need assistance or any other help, please feel free to open a new support ticket, and we will be more than happy to assist.
Thank you.