Rick, those cable lube tools work great. To handle the dribbling I simply wrap a rag around it. Make sure you have removed all the burrs in the lever, perch,and adjuster at the handlebar, as well as at the actuator in the case. The cable must move freely.
Don't use grease or any thick, heavy lube. These get pasty and tend to hold grit. this adds to stress. Dry lubes such as graphite clump up with any hint of moisture and have the same issues.
If you don't have a genuine motorcycle specific cable lube, just use WD-40. WD works great in this application.. Also, every 2 or 3 or 4 weeks hose down the upper end of the cable with the WD. Aim the nozzle into the opening where the inner cable exits the outer housing. Work the lever in and out as you squirt. A lot of lube will work it's way into the cable.