J120 is a notorious connector. All the GI strings are powered by this connector, and it almost always will be burnt, if not already replaced.

Sadly, sometimes as you have found, it does not get repaired properly...

The good news is that changing from #44 lamps to #47 will dramtically reduce the load on these connectors, and the fact that in home use they will not be on 16 hours a day means once fixed they will not need any attention in the future...

The bummer here is that J120 is only for GI, so won't be related to the idol lock problem :(

The idol lock solenoid is solenoid 6, Pin 7 on J130 with a violet/blue wire, if that helps the chase....

Cheers
Jacob