Dave, I would have likely given the treasure to the second person as the first person didn't actually play out any searching or even pay attention to what he/she was searching.
IMO, it takes as much time to search someone as it does for that person to OOG pull out treasure - so if the first searcher runs off or attacks something else while I'm digging out coin, and Sneaky McSneaksneak comes up and searches me, then the person gets it who is the one who hangs around long enough for me to get my treasure out of my pouch. Alternately, if I'm of the "crumbles to dust/disapears/goes gaseous at 0 body" variety, 8/10 times I will put my treasure on the ground - even if someone says that they are searching me, because, you know.. pile of dust on the ground.
I have yet to see a heated argument about any of this... but it seems that others have, perhaps a two line specific action about searching could be put in the rulebook..? "You must kneel, place a hand on the shoulder of he target of the search and say 'I search you' and then wait X seconds to complete the search." *shrug* Is it that much of an issue? I'm not sure that it is. But I have seen very inattentive searchers get annoyed when I haven't handed them coin, AND I've seen NPCs who've been totally annoying about searching, a hard and fast rule wipes all that out. But no amount of rules will wipe out asshattery.
The 6 or 8 times I've ever searched a creature as any of my three PCs I've crouched or kneeled down and looked at the person I was searching and informed them that I was searching them. I typically give a bit of a narative "I check your weapons.. does your armor look salvagable?.. I look for potions or alchemy.." I'm detailed and if asked to describe my search I do so and generally have a good time with it. I've also seen people searching and the NPC being searched puts them through the perverbial wringer "describe your search.. no .. no.. no.. ok, wait 5 seconds.. you find nothing."
On the other hand, from the NPC side of thing, I rarely ask people to describe the search unless it's something that I think is not obvious (like, for instance if I'm wearing armor or holding weapons that can be taken), I typically start pulling out my treasure and whomever is the person to touch my shoulder and tell me they searching gets it. I *do* get to be a bit of a stickler if someone is standing and not looking at me, though, and will typically wait for them to look back to me before I hand off treasure - because saying "I search you" and scanning the field of battle for foes seem to be conflicting actions to me.
HtM