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That is a common-enough problem with STX000 autopilot systems. I've heard of it and dealt with it several times before this in just the past three years.
In sum, I advise you to first check all connections.
(You might have a cable that's a little loose, a little damaged, or a little corroded at the connection.)
Inspect all cables in the autopilot system, including the ST6000's connected cables, the cables to the motor that drives the actual steering, the autocompass if there is one, etc.
Make sure none of the cables is severely bent, cut, damaged, etc. at any point along its length.
Then disconnect each connector, one at a time so as to not confuse how to put the connectors back properly - which can happen when you disconnect more than one at a time - and scrub each side of the connection with a clean dry brush, then wipe down the metal on each connection so that the metal shines, with a clean dry rag cloth, then re-connect firmly, and on to the next connection/connector.
After which - since the system gets placid again when you switch to standby - I would suspect you simply have a disordered autohelm.
But the inspect-scrub-and-clean process is necessary before so concluding. An obstinate tendency to steer to one side, is typical of an autocompass system that thinks it is off-course, e.g. owing to a defective autocompass indication. So check that your autocompass isn't 'stuck' too, before replacing the autohelm or having it serviced etc.
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