I'm probably way off base here, but I just wonder if one of the reasons the 2nd murder took place was because he knew the police were on a wild goose chase. A month before Caroline was murdered, Wendy Knell's murder featured on BBC Crimewatch around mid Oct 1987. That was the first time they showed the photofit which obviously wasn't him. I just wonder that having seen that Crimewatch episode he decided to strike again and, in a way, taunt the police.
Yes, Caroline's struggle/screams may have spooked him away from a 3rd murder...but I do wonder if that photofit and CW episode prompted him to strike again and near enough 4-5 weeks after the Crimewatch episode. It's possible that the Great Storm, a few days after the CW episode aired, may have delayed him a little.
You can tell in that CW episode that the police were short of leads with Wendy's murder:
The details of how they made that photofit is mentioned in the above CW episode. The circumstances behind it are just as creepy as this Fuller bloke, but could be just an innocent and concerned member of the public who was aware of the prowlers at the time.
Timeline:
CW Episode: Oct 13th 1987
Great Storm: Oct 15th 1987
Caroline attack: Nov 24th 1987
Just to recap on the photofit:
1987 Photofit
View attachment 320920
Fuller, 80s picture