I think Intruder may have it. Poor bonding/shielding with HIRF or RF fields play havoc with other systems / indications if bonding and or shielding is poor.
We nearly had to set down in the Iranian boondocks many moons ago with a dodgy engine that turned out to only lose oil pressure etc with HF transmissions
. Lucky the travelling ginger beer was a good radio bloke
It can be a bugger to find offending wire / bonding point though.