I don't know if gutters is the correct term, but the rubber strip at the edge of the top around the windows that diverts rain from running off the top down the windows (or onto people if the door is open). That rubber strip has broken off in places, mostly where the top folds back on itself.

Has anyone made a jury-rigged strip to keep rain from dripping on them when the door is opened?

 

Are you talking about #9 and #8 on the diagram below? If not can you post pictures of what you're describing?

 

Do you have a pic ? MINI Convertible owner here also.

Thanks

 

i think they are referring to the small rubber j mold that looks to be stitched into the top along the sides
forms a small drip rail
not the items shown in the diagram, i think that is the window molding