There are two different re-punched mint marks for the 1909-S Lincoln cent. One is RPM-001 (vertical re-punched mint mark) and the other RPM-002 (horizontal re-punched mint mark). RPM-001 is the scarcer of the two different re-punched mint mark varieties for the 1909-S Lincoln cent.
The S mint mark on the RPM-001 variety has strong re-punching towards the South East of the first S mint mark. The second re-punching is fairly prominent and can be easily seen with a 5x magnifying glass. RPM-001 is much scarcer than the more popular (RPM-002) re-punched mint mark variety.