After a 2000 mile trip with my bike on the top of the car my left shifter is gunked up from salt and road grime.
It is down shifting real slow or just does not engage. I really do not want to disassemble the hoods as I know these can be complicated.
Motobecane Fantom Uno-Got rid of the rest when I moved to LA:(
well you can try the following-
Use a hose with a presure nozzle to wash up in the brake as best you can, make sure to peel the hood back and get in there as much as possible. Move the levers around as you wash to help dislodge the grime. Let it dry and see if that worked.
Take the lever off the bike and run it under the sink doing the same thing-alternately you can submerge the lever and shake it around while flicking the moving parts.
After it dries you can lube up with some WD40.
make sure to let it dry out as much as possible before lubing or reinstalling. Keep in mind that while most of the lever is Alloy rubber and plastic there are some stainless steel screws, pivots clamps etc that can rust a little so you want to make sure you dont trap moisture in there.
If that doesnt work you will have to take the lever apart.
BTW-use hot water if you can, it will help losen dirt that is stuck to the internal lubricants that are in the moving parts.
STI shifters do not like dirt, water, crud, etc. Salty water is probably the worst you can put into your shifters other than sulfuric acid.
Try flushing them out with lots of WD40 or similar. The cable housings may also be full of crud.
I recommend that you not try to take them apart.