That circle in the middle isn't paint, it's - for lack of a better term -
glue.
Actually, a combination of adhesive and waterproofing. There is a longwire
VHF
antenna that runs from there to the spine just behind the flight deck.

TSg Bill

Most of the C-130s I worked on were the bubble top HC-130P and HC-130N and I
seem to recall the long wires went to the leading edge of the vertical stab.
Come to think of it the bare panel seems to have disappeared on the ones I
worked on long before we went to gray. Maybe it was a change on ours.

Many thanks.

Dan, U. S. Air Force, retired