Thanks, clearwater, for the generous offer. People like you are a credit to this forum! What's more, you've managed to find the right term -- so these things are called glove hooks!? Hunh. Excellent!

I think to use the item in the link, I'd have to run something through the ring to attach the hook to one glove, and that may require either restitching or breaking the plastic D-ring to replace it with a metal ring that could be bent open and closed.

I ended up getting this, which looks very close to the hook that broke. The measurements also seem to be the same.

http://www.ebay.com/itm/1-2-O-Ring-Glove...=item8019f9c931

Thanks again, everyone, for your suggestions! What a great resource ETS is!