It HAS to be a ground issue. The lights are not connected with the turn signals. The signals power come from the turn signal switch, the lights come from the light switch. The only common connection is the socket ground which is the ground plane of the cluster pc board
The only other possible common source of the problem is the ammeter/ bulkhead connector/ power distro has a drop in that circuit. This should be noticable on other accessories such as heater/ radio/ etc