However, as activity on the nearby 27 MHz CB band shows, 12 metres is probably open more often than it might appear. A good check are the IBP CW beacons on 24.930 MHz. You could also try WSPR. Setting up a WSPR receiver would be especially welcome as there seem to be more stations transmitting than receiving there in recent times.
The scavenger interested in 12 metres will be on the hunt for old 27 MHz CB antennas, which with a little lengthening could be set up on 24 MHz. Other options are to take the dimensions of a 10 or 15 metre design and scale up or down accordingly. Or you could build your own from scratch. Here's some ideas.
3 element LFA antenna for 12 metres by G0KSC
28 and 24 MHz 3/4 wave delta loop by KL7JR
Lengthening a cheap CB antenna for 12m by G1EXG
Low cost magnetic loop for 10 and 12m Video by RadioHamGuy
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