My thought is that this is stained paint from some kind of liquid spill that is more than just plain water.
If a light wash and clay didn't work then you are going to need to progressively move to more aggressive steps.
1-Pre-wax cleaner (Mother's Pre-wax cleaner, Pinnacle Paintwork Cleansing Lotion, Wolfgang Paintwork Polish Enhancer, etc...)
2-A medium to heavy polish (then a compound if that doesn't work), preferably Wolfgang or Menzerna if you have a DA polisher or any good quality polish with a rotary. Some spots should definitely come out after this step but be prepared for a wet sanding activity should some spots remain.