The only time that we know of that Eddie alerted at the car was outside the drivers door. We saw on the video Mr Grime stating that he was not going to put Eddie inside the car but why not? Surely the whole point in the exercise was to find out where in the car there was cadaver residue if any?
I find this a bit of a mystery tbo.
It's not a mystery if you accept the idea that Eddie was the GP and Keela the blood specialist (it's the haystack and needle analogy that was used to describe the duo in the press ages ago).
Try it the other way around. Keela can pinpoint tiny amounts of blood. When she does, that could be significant in terms of forensics. Great, but time-consuming - as on one has time for a dog to sniff millimetre by millimetre over a large area. The police had their general zones to check, Eddie was supposed to react if anything seemed to be of interest, and Keela was wheeled in to try to spot any trace of blood which might provide potential forensic evidence, hence saving time.