Hello Nelly,
The third hammer is also for 3 per rev. vibration, but for lateral. I have found with most 120's that if the aircraft needs work on the lateral hammer, the ride quality will have an "edge" to it that is more noticeable than a vertical 3 per. (Of course, I may just be the overly sensitive type when it comes to laterals!)
What kind of equipment is your Engineer using to tune with? Do you have the later style hammers with adjusting washers or the older shifting mass style? I would recommend upgrading if the answer is the older, as the newer style does make for much easier/more effective tuning.
Regards,
Rigidhead