That’s good you found the problem and posted the fix; you posting the fix may help someone else in the future.
Just one word of caution thou; you said.
I wrapped it around the other wire
You should maybe take that connection apart again and solder or use solderless crimp-on connectors to rejoin that red wire to where it came off.
If that connection you made by wrapping it around the other becomes loose, it could cause it to become hot & burn.
Not only causing your problem to return but possibly burn the wiring harness; worse yet the whole car.
Dan.
Canadian "EH"