I am looking for the meaning of 石松 in this context (待ってください用心棒なら この石松が) but I cannot find it anywhere. Also, this sentence is one that was interrupted, hence the abrupt "が".
石松 is the speaker's name. He's offering his service as a 用心棒.
You said he got cut off, so the sentence could have ended something like
待ってください用心棒なら この石松がやります or つとめます。
Or, if he is using 敬語、
There are hundreds of possibilties, so these are just some examples