There is a 5, 9 & 12 volt dc regulator on the chassis that could be causing this. Three legged transistors on small heat sinks. I f you look at the chassis from the rear of tv, is two boards.The one on the left has these reg. transistors. Usually the 9v regulator is bad and a 35ufd @ 50v capacitor near it is bad. From the tuner as ground check the third leg on the regulator for less than 9v dc.
SOURCE: JVC AV-60D501
From what you're describing your focus block is probably failing JVC p/n#129P059050. It's probably also very vibration sensitive. They're about $80.00 dollars and they are also interchangeable with the Mitsubishi focus pack p/n#920p016010. Not a difficult repair - we do about 5-6 a month. Real easy in-home repair. Hope this helps. Bill
Usually answered in minutes!