How can I locate a short in a 24V central A/C circuit?
Use a Network Cable Tester
To find short- and open-circuit conductors in any low-voltage multi conductor cable, I recommend

isolating the cable from all devices (i.e. disconnect it from the furnace/heatpump/AC and thermostat), and

using a network cable electrical tester and RJ45 breakout adapters to test it.


RJ45 Breakout Adapter
You need two of these.  One for each end of the cable.
This is one style:

Here is another:

Network Cable Electrical Tester
You need one of these 2-part devices.  They are very simple and cost about $10.

Making the Connections
Attach an adapter to each end of the cable under test (CUT).  Decide on a mapping between CUT wire colors and pins 1 to 8 marked on the adapter.  The mapping can be arbitrary, but you should use the same mapping at both ends.
Connect one part of the tester to the adapter at each end of the CUT.  Depending on the adapters and tester, you may need some short network patch cables to do this.  If you do use patch cables, make sure they are straight through and not crossover cables.
Performing the Test
To perform the test, you just switch on the tester and confirm that its lights flash according to the expected pattern.  You will need to read your tester's manual to determine the expected pattern and interpret what a deviation from that pattern means in terms of short- and open-circuits.  This video shows one of these testers in use including the flash pattern for that particular tester.
Limitations
There are, of course, limitations to this method.  Here are the ones I can think of off the top of my head:

Limited to 8 conductors at a time
will not detect shorts to ground via other cabling
can be confused by even very low voltages applied to conductors by shorts to energized circuits (although you'll probably still learn that there's something awry)