My go-to solvents for removing old adhesives are Naptha and Xylene. I
have never used "Oops" as suggested by MW but having just googled it,
I see that 2 of its four ingredients are Naptha and Xylene. The other
two ingredients are Ethyl Alcohol (which probably wouldn't be
effective against the OP's brown crud) and Toluene. Anyway, Naptha
and Xylene are readily available at the paint department of the big
box stores. Acetone often works well too but it's annoyingly volatile
and Acetone will more frequently have deliterious effect on the
underlying surface.