The un-suspected fault with a broken connection to one leg of the Nav antenna would normally show up when testing the system as insensitive operation. Typically you're looking for the fail flag not to appear until you attenuate the test set by at least 55dB, and with a leg disconnected, it normally fails at 30-35dB down.
Presumably you mean standing on the aircraft axis when doing the test.
It will still pass if the tester just happens to be standing on one side (the "right" side) of the aircraft, because on the TB20 the vertical stabiliser masks the other antenna pretty well - so well in fact that a few miles from a VOR you cannot hear the ident at all if the VOR is exactly in the 3 o'clock blind spot.
On an EASA aircraft maintained under CAA LAMP, this test is done on every annual,
Not usually (in that way) where I am standing
but on most N reg, there is no requirement in the maintenance schedule
There is a mandatory FAA VOR check every 30 days, which is more relevant than a ground test, because the pilot does it himself so he knows it has been done. Whether that detects anything depends, again, whether you just happen to have the VOR in the right place when doing it. But it is arguably more likely to detect it than the ground avionics test, which is normally done with a man standing next to the aircraft, holding the test set.
If you fly say 20nm away from the VOR, and then do a reasonably tight (but with not much of a bank angle) 360 orbit while listening to the ident, the duff antenna is quickly revealed. That is how it was finally detected. This is a potential killer - even without the KN72's contribution...
I do recall seeing odd effects, over the years, on NAV1, on the 30-day VOR check, but they could never be reproduced, and anyway I almost never use NAV1 for VOR. The fault must have been there for years and most likely while it was G-reg on the PT CofA.