I know Garmin do quarter turn mounts on some of there gps units but not the Etrex but found a file on the interwebs for a 3d printed one and all you have to do is buy the bit that fits on the stem, 3 quid from ebay

One of the lads that work at my local bike shop has a 3d printer and I asked him if he would have a look at the file for me, he's a smart cookie and said the quarter turn 3d printed bit would not be super durable but he could make the slide mount that bolts to the new stem cap if he alters the file a bit.
This is the first test one, he is getting some more durable plastic for the new one but so far it is working very well.
This first picture is the quid stem cap.






