Stereo Headset - Handheld Radio

Background: Single place, Day VFR.
I picked up a Sigtronics Stereo headset from our chapter's "Free" table.
I bought a new IC-A24 radio.
I only hear in one ear cup - at first I thought it was a case of stereo-this and mono-that. But all the connectors are 3-conductor, so I'm assuming I should hear on both sides.
Is that a correct assumption, and how would you diagnose the problem? (I'm a long way from the airfield, or else I'd try the headset on another plane.) Thanks.

-glen

Three conductors is right for the headset plug on a stereo headset. The radio adapter may be only mono. You don't say which model headset this is, but the later ones have a Mono/Stereo switch on the little plastic piece where the mic/headset cables fork off from the headset cord.