Hum out of right speaker only while on analog

I have a hum from my right speaker only that happens only when the tone arm is within 1/2" of the rest for the arm.
I can also create this hum by moving the arm out of the rest.
I have tried other interconnects, then switching them, I have checked my ground wire and all 4 head shell leads and all seem to be good.
Digital play back is perfect, no hum.
Checked my RCA soldered joints and all seem good.
Once I had this hum also while playing the first track of a LP but it has never happened again.
Once I am 1" away from the rest area for the tone arm all is perfect and playback is perfect, no hum at all.
I have no way of checking the leads running through the tone arm to a Din connector. This part is out of my league.
Any thoughts on why just the right channnel and just in the above mentioned position?
All leads to the cartridge are good.
Any help would be appreciated,
I had the same issue when I was using a Bellari VP129, and then a Grado PH-1. I did EVERYTHING and still I had the hum, and sometimes I would actually hear faint music, too. It was like I had some sort of weird antenna. I finally went to a Cambridge 640P which was completely silent. Then I upgraded to a Sutherland Ph3D with the same results.
I had a similar problem one time, and mine was resolved by running a ground wire from the preamps chassis to the amps chassis. Go figure.

Dave, What kind of turntable/arm is it?