Wolters isn't sure Brueckner actually abducted Maddie, he's only certain that he murdered her, apparently, & he presumes she was killed quite quickly.
But Brueckner was still hanging around the Algarve for at least a week after May 3rd, rather than skipping town pronto.
There are reasons for the fact that it took fifteen years before Madeleine's case had any hope of resolution.
The man who wasn't in when the police came knocking at his door in May 2007 managed to keep a low profile until 2013 when a witness identified him after watching an appeal by Kate and Gerry.
Pity the police didn't keep following that up since you say he "was still hanging around the Algarve for at least a week after May 3rd".
He remained 'hiding in full sight' until another appeal by Kate and Gerry in 2017 flushed him out into the open although we only heard about him in 2021.
Seems nobody paid him any attention during his sojourns in the Algarve which seems to have been his favoured stamping ground for all sorts.
It is where he committed the heinous torture and rape he was jailed for. His victim didn't get justice in the Algarve. The Germans had to do that for her in a German court.
What a charmed life this well documented career criminal led in the Algarve. The INVISIBLE MAN for over fifteen years with a coterie of ex-police leaping to his defence in the Portuguese media when his cover was blown by a foreign police investigation.