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Martin, my comment was admittedly cryptic, since I generally won't make much effort for anonymous users. But to elaborate slightly, I was referring to the case $F=\mathbb{Q}$. In this case, with the help of a tubular neighbourhood, we can see that $j_*F = \mathbb{Q}$ if $q=0$, $R^qj_*F= \mathbb{Q}_Z$ when $q=2 codim(Z)-1$, and the other direct images are zero. Then it is not hard to see that Leray reduces to the above "localization" sequence given in excision in algebraic de Rham cohomology