Do not use tape.
Use thick gel super glue ( CA glue ).
Get a flat wooden board ( or card board can be used ), wax paper ,scotch tape a couple of pins and the super glue ( CA ).
Tape the wax paper to the board.
Tape the c/s to the board flat as possible with split on top.
Apply the super glue gel to the inside edge of the tear.
As quick as you can pin the tear flat going through the edge of the strap on an angle both sides down to the board.
You can allow to dry or use a kicker to quick set the CA glue.
I have done SEVERAL repairs to chinstraps and tears in felt haubes
When done the repair is almost undetectable and will be the strongest part on the strap.
You must use the thick CA glue ( gel )
If you use the thin capillary action will happen and the glue will set before the pieces are able to stick together.