Yes, the "black tape" is, as suggested, the sealing rubber from the pitot/nose join. I have replaced many. There is a reinforced bolt hole through the middle, and it bolts just above the nose lamp assembly. The lamp is visibly trashed, so no surprise, it has migrated down the pitot head. In other words, normal.
Oh, and onother thing - if photos are to be believed, the photo of the A/C taking off had both crew wearing white helmets - If, as has been suggested, the pilot was RAFAT, he would, I am sure, be wearing his RAFAT "arrowed " helmet.
For info, the aircraft stored for future Red Arrows use are at RAF Shawbury, not Valley as many may believe...