TRS vs. TS cables, continued

Hi. I'm new here. I'm a retired electrician with some background in electronics, from amateur radio, but not audio related. I'm just beginning to get interested more in the audio field since my son, 25 (I'm 62), is fixing himself up a recording studio in his bedroom.

But to the topic:

My son is using one of my 2 electric guitars at times (He is a classical guitar student, but is beginning to do some experimental stuff on my electrics, using a "boomerang" loop pedal.)

He's been using my Danelectro guitar up until the other day. It has single-coil pickups. He was getting hum (goes with the single-coil territory), noticing that the direction of the guitar affected the hum, as it picked up what I'm guessing are 60 cycle signals, acting as an antenna.

I suggested he try using my other electric, a Hofner, which has "hum-bucking" pickups. He tried it, and noticed something strange.

He's been using TRS cables for the guitars, since when he made some inquiries over at the "gearslutz" forum, they told him that it shouldn't matter, since the cord lengths are short, and tried to describe how a balanced vs. unbalanced system works, and how anything in the system that is "unbalanced" will just cancel the benefit of having everything "balanced" in the other part.

But here's what happened:

When he plugged into his little acoustic amp with a TRS cable, he could hear hum whenever he lifted his hands from the guitar strings, and no hum when he kept his hand on the strings. This is WITH the guitar that uses "hum-bucking" pickups.

Then, he tried using a TS-only cable, and voila, no hum. He tried it with my amp, and found the same results.

Why does a TRS cable cause hum, when used from guitar (with hum-bucking pickups) to amp, where a TS cable does not cause hum. With the single-coil guitar, hum is constant, but with the "hum-bucked" guitar, hum is only apparent when using a TRS cable, and lifting one's hand from the strings. The hum disappears completely with a TS cable.

"Lucy,,you got some 'splainin' to do."

Thanks a bunch, let's do lunch.
Robert