Don't try cloth tape first - that's the hardest stuff to work with. Start with a tape that is somewhat stretchy. Overlap turns by 1/3 and try to stretch the tape as you go around bends and around the brake levers. You can either start in the middle and finish by putting the excess inside the bar and plug, or you can start on the end and finish in the middle with a wrap of electrical tape. Sometimes it work well to take 2 small sections of tape and cover the back side of the levers before you wrap.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72