In this video I walk through troubleshooting an Sync Circuit with an Oscilloscope. I use a Centipede board, but this should help you troubleshoot any Sync circuit on arcade games as the concepts are universal.

The 82S129/131 replacement shown in the video is available at

http://www.arcade-cabinets.com/board_hacks/82S129-82S131-to-27512/

Replacements for the similar 82S131 are available at

http://www.arcade-cabinets.com/board_hacks/82S123-to-27512/