Reasons Why can't you  connect to your Google account on an old Android phone:

• To be clear, there are a variety of reasons why you can't add a Google account to Android. The issue could be caused by a variety of factors, including the well-known Google server issue, flaws or corrupted caches in Google Play Services (or other core Android apps), obsolete software, and so on.
• Start by rebooting your phone and then going through the procedure again to see whether you can still add a Google account to Android.
• If not, perform the following steps to delete the cache and data for the Google Play Services app.Take your phone out of your pocket. Select Apps & Notifications from the drop-down menu. Choose 'All Apps' from the drop-down menu. From the list, locate and select Google Play Services. To reset the Play Service app, select Clear storage (or Clear data).
• Reboot your phone, then try signing in to your Google account to check whether it now works.

Read More: How do you add a device to a Google account?