Anyway to rewire a ps5 fan?

Hello,
Recently picked up a ps5 with the fan connector ripped out and then they’ve had a shoddy attempt at repair one of the pin pads looks to be gone and very little to solder to … cam anyone explain what each wire in the fan does and if theirs a way to wire it to.

3pin fan unit, RED=12v. BLACK=ground. GREY=pwm

Would the ps5 fan run without the pwm connect so it just runs at full speed?

No. I can confirm that the fan will not spin at all if it gets no pwm signal.