After a bit of detective work I think that I've found Fazal Mahmood in action!
Unfortunately the footage has no sound so there is no commentator to tell you who is bowling.
However, the footage shows a right arm medium-fast bowler bowling a couple of overs to Sobers and Hunte (?) during day 5 of the West Indies V Pakistan Test, Sabina Park 1958.
The scorecard shows that the Pakistan bowlers were;
Fazal Mahmood (right-arm medium fast)
SF Rehman (leg-break)
Nasim ul Ghani (left-arm medium)
Haseeb Ahsan (off-break)
Abdul Kardar (left-arm orthodox)
4th Test: West Indies v Pakistan at Georgetown, Mar 13-19, 1958 | Cricket Scorecard | ESPN Cricinfo
Therefore, Fazal Mahmood must be the bowler in action by exclusion. The quality of the film is quite good, so definitely worth a look.
WEST INDIES CRICKET RECORD BY SOBERS - NO SOUND | AP Archive