I don't know if this is the right way or if it is going to fall off in the next week, but it seems to be working and doesn't look bad.
I used the extra behind-the-brake-lever piece to figure out the angle that I would need at the end of the bar. I cut that and transfered that angle to the real tape. I put electrical tape with the sticky side out around the last ~6" of the bar for some extra stickyness in that area. Then I wrapped the bars in a way that I believe will tighten the tape while riding. I laid it on thick to make up for the shorter wrap area as compared to drop bars.
I finished both the closer to the stem and the end of the bullhorn with electrical tape that matched the color scheme of the tape (black near the stem and red near the end in my case).
One thing I did was add a dummy brake housing on the right side before wrapping. I didn't like how small the bar felt in my hand or the asymetry with the brake only on the left.
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