Some wheellocks had strange metal handles along with a wooden shoulder rest looking thing off to the side. To my knowledge, this is a development unique to wheellocks, not really seen in the earlier matchlock or later flintlock (But I may be wrong here, this is just my assumption)
Why were these handles used? If they were effective, why did they only see major use in wheellocks, and not other forms of firearms? Lastly, why might they have fallen out of use?
For 16th c. and earlier matchlocks and wheellocks , the stocks were pretty heavy and bulky. That's a triggerguard: but it's also a grip. One finger on the trigger, the rest on the grip ( notice the notches for the fingers). As the 16th c. stance was also with the elbow up it would be much more comfortable and allow the triggerfinger to be better braced.
Later gunstock design changed; as the calibers became smaller and the barrel lighter the stocks could become lighter and thinner as well, and it was possible to grip the hand around the whole wrist. Even later in the 18th and 19th c., , though , some triggerguards could have extensions that were rests for the fingers, and later pistol-grips became ( and are still) popular for sporting guns and not a few military rifles.
