I have a Unicomp Classic 101 from about 4 years ago that has very crisp clicks but absolutely no pinging. I also have a Mac-version keyboard from them that pings quite a bit. Over a year ago, I asked Zack at Unicomp why some of their buckling-spring keyboards ping and others from them do not. Zack said they have no idea why some ping and some do not, and have no way to control it.
Some vintage IBM-made M's ping a lot, some ping very little, most are somewhere in-between. Lexmark M's seem to be pingy in general IME. There doesn't seem to be a distinct pattern, and I find that rivet condition and bolt modding (or not) have little predictable effect on pinging; although applying extra tightening torque on a bolt mod does seem to reduce pinging -- but often resulting in softened clicks as well. IME if a Model M pings before a bolt mod, it will do so afterwards as well, provided that the clickiness is preserved in the bolt mod by not over-tightening.
Pinging, or lack of it, in a buckling-spring keyboard may be the result of a complex interplay between how firmly-clamped the layers of the switch assembly are, the exact alloy and stiffness of the springs, thickness and alloy of the steel plate, the exact plastic composition used in the barrel frame (or individual barrel housings in a Model F), the type of blanket -- original IBM black or Unicomp white latex, and other subtle factors such as the phase of the Moon, planetary alignment, and Zodiac sign of the user...