If apps fail to load due to outdated Google Play Services, the most reliable method is using a lightweight browser. Old YouTube app fix (Android)
Because you cannot use the Google Play Store for this, you must sideload the application using an APK file. Follow these steps carefully: Step 1: Enable Unknown Sources
Lightweight Performance: Stripped of modern bloat to run smoothly on older CPUs.
Google dropped support for the older legacy APIs that Android 4.1.2 relied on to communicate with YouTube servers.