Yes, you can make a symmetrical taper effect by using ‘Invert Taper’ + Tip Lenght. Do the following:
1. Build or re-build the TS geometry with all the Extra Features on (Taper, Tip, Slice).
2. Go to TS Edition section
3. Check ‘Invert taper’ on.
4. At ‘Tip Parameters’ group, go increasing the ‘Tip Length’ value while you see the result in the TS mesh until the wider part of the mesh is located at the middle of the path/mesh.