In 1984 I was a US Navy Diver stationed on board the USS Preserver, ARS-8. We were on a routine excursion to Pensacola, FL from our home port in Little Creek, VA to recover the wreck of a downed Navy Trainer, A-4 I believe.
En route headed south just east of Cape Hatteras we noticed that our stern running light was out and needed to replace it as dusk was approaching. The aft third of an ARS is all salvage deck and diving space (hydraulic and electrical gear below along with the diving locker) and as such was our responsibility for all maintenance and repairs.
Not a big deal as all that was needed was to lower the flag staff and replace the bulb. The evening meal was being served on the mess decks and while we were changing out the bulb and BS-ing when we saw what appeared to be a flare off to the east.
Oddly enough the 'flare' rose in the sky, disappeared or extinguished then reappeared and whizzed off in a near vertical motion. This was most unusual, but since we thought it was a flare, we reported it to the bridge as a normal course of procedure. We were speculating on the odd occurrence and why a 'flare' would behave in such a peculiar manner.
Could it have been a UFO? Our fellow sailors were now coming out of the galley, one by one and were gathering as we were describing what had happened. For the most part everyone thought we were just being ignorant and dismissed our speculations as just that.
By now it was dark and a very clear night. While in the midst of our banter between divers and the rest of the crew, one of the non-partisans to our little story became pale and his eyes opened as if he had just seen a ghost. He pointed into the sky off the starboard gunwale and we all saw it, a red orb.
This light reminds me for all the world like the little trailing red UFO on Close Encounters (I am just watching it for the umpteenth time which is what caused me to look up 'glowing red light UFO' on Google. This red orb hung with us for awhile and seemed to be about 30' in diameter, though it had no real form.
Our boat only ran at about 13 knots, so this thing was just keeping pace and made not a single sound. We all hustled up to the signal bridge to try to catch a glimpse through the "big eyes", the mounted binocular telescope used by the signal watch.
While on the signal bridge (which happens to be directly above the bridge of the ship where Ops and the Captain are situated) we could hear radio chatter from Coast Guard vessels and other vessels calling the Preserver to inquire about the contact that was showing exactly on our position.
In almost an instant the red orb took off at what seemed like an unimaginable speed again with no sound. We spent the rest of the night looking up towards the heavens, but never saw another thing like the red orb that would mark its place in our memories for the rest of our lives!