Many thanks, wigglyamp

and all.
I will do more tests.
Presumably the SWR can be tested by pulling the radio out and sticking a tester into the now exposed RF connector in the back of the tray? Otherwise, the cable runs from the back of the tray to a bulkhead BNC on the centre stack module (that part of the cable, about 3ft long, is inaccessible without pulling the whole centre stack out

) and from the bulkhead it runs to the antenna directly. I know it is not RG400 and should be, but I have not had this problem before.
There seems no evidence that TX is affected.
Also I wonder why a bad static wick or bonding or a bad ignition lead would have no effect on the #1 radio.
I will swap over the two radios, but also do a ground test with distant stations with the engine running (should have thought of that).
The #2 radio is only ~ 2 years old and was bought brand new. Normally the KX1x5
A are very reliable radios.