Very few (if any) headset makers use brown grease, so you're seeing a mix of grease and water, and the brown color is because of rust. One reason that many bike mechanics prefer a lighter colored grease is that they can use the color as an indicator of condition, ie dirt or rust.

If it's coming off the lower bearing, you're seeing the result of water spray off the front wheel getting blasted into the lower headset assembly. This is common on some headsets that lack a decent seal or long skirt there. The bearings seal isn't adequate to keep water out, so if it's sprayed into the area, it'll get to the bearing.

You can improve things, but how you do it depends on the headset. On some, you can fit a large rubber band (I use the one that comes on Broccoli) around the lower headset assembly so it closes below the crown races. On others, a disc pressed on below the crown race reduces spray entry, and on some headsets you can trap an O-ring between the crown race and heat tube or bearing skirt.

Either way, you're choice it to improvise a better seal, or drop the fork, and inspect, and grease the lower bearing every 6 months or so.