My mind keeps coming back to the tools and lipgloss which were found. The police
very quickly distanced the find from the search for Libby, which was good enough for me at the time, but now I'm not so sure. They were found on Feb 3rd, before the arrest and, presumably, before they had PR's DNA and prints on file. There was a large media gathering present for the find, and it was quickly reported, so the police
had to say something.
I think that he has initially seen LS closer to her student accommodation and subsequently followed her along Beresford Avenue towards Beverley Road. I can't suggest any reasons why the tools and lipgloss was discarded, other than perhaps in preparation to win someone's trust. He may well have intended to go back for them (it would be totally valid to ask why they weren't just put in the glovebox or boot etc). Lipgloss could be perceived as being a fairly intimate item, but one which you could easily come across - a quick thrill. The items were discarded in the flower beds immediately to the left of this image:
Google Maps
There's a clear sight of the bench, and at least a decent view of the parking situation on Haworth. From there, it's a quick right at the junction with Cottingham Road and onto Haworth Street. That could've taken less than a minute, leaving PR in a good position to get a better read of the situation (passersby, GB etc).
The tools may also have had no relation to the lip gloss at all, but that doesn't make them irrelevant.