Good title/subject Bullseye....a varmint pistol is different things to different people.....
For what we do here on the high desert shooting our favorite varmint, the ground squirrel in the alfalfa, a 'varmint pistol' is usually a belt gun worn or on the bench while shooting CF varmint rifles. The handgun is used for those pesky ones that pop up 10 -25 yards from the bench, daring you to shoot them. I've had the same thing happen out for pd's also. The usual caliber is HV 22LR HP's, but both 9mm and .45ACP's have been known to be deployed on the little crop-eating critters too.
Revolvers or auto's, it's all good, and one is always within reach:
I've carried a 1911 in one flavor or another since 1965 and my return to The World in 1968 carrying as a citizen. When in the rat patch, one of my 1911's gets a Kimber rimfire conversion installed on either a 5" full size, 4" Commander size, or one of my 3" carry pistols. That gives me the same trigger and manual of arms in the field for familiarity. Big fun, highly effective to boot.