Gretsch 6120 buzzes unless I am touching one of its metal parts. How to fix it ?

It sounds like you have a bad ground.

First… did you try a different cable?

The hum going away when you touch hardware or the strings is the instrument functioning normally. You're adding yourself as a ground and also as a big fleshy RF shield, and that is why the hum drops. The question is whether the initial buzz is excessive or not.

Plug the guitar in, and touch each electrical one by one, reaching under knobs to touch each pot, pickups, switch, and so on. If touching any makes the buzz INCREASE, that means it is not grounded. If it decreases, it is grounded. If you have a multimeter, you can do it with the probes. You should have continuity from all of those parts to the sleeve of the jack.

If all of that passes, the normal solution would be to add shielding. Not an option for a hollow body guitar. You could rewire it with better wire. But, that's very time consuming, and expensive if you have to pay someone else to do it. That leaves the final option: live with it.

As funky said, your ground is just fine. But funky is mistaken that the your body is grounding anything, in fact your body is a sort or relay transmitter for the source of the noise and touching the metal parts of the guitar is grounding your body which reduces the noise. Sometimes shielding works, for guitars where cavity shielding is not possiby shielded wiring might help, but sometimes your only remedy is to find the source of the noise and switch it off. Could be an old TV or monitor, dimmer switches, fluorescent tub lights, air conditioning or a transformer somewhere (could be in your house, or a few houses down the street in some cases).

The reality of all this is some guitars are simply 'tuned antennas' that pick up more noise than other guitars do. And amps simply amplify. Desirable signal and undesirable noise all get the same indiscriminate treatment from the amp: they get louder as you turn up the volume.

If you have a guitar that is just more noisy than your others, you can try a few things. Shielding can help, but not always. A common thing to reduce noise is to remove any 'extra' wiring in the guitar circuit. For example, extra length on a pickup's leads. Doing this reduces the gain of the "antenna" and can greatly reduce the noise.

The reason I mentioned grounding is that I had a buzzy Strat that also quieted when I touched the strings, etc. It was my first Strat so for a couple years I unknowingly accepted the situation.

I was in the trem cavity and noticed the ground wire to the claw had a seriously cold solder join. I reflowed the solder and viola! The hummy/buzzy thing was dramatically reduced.

$.02

😊

The way I think of it, both funky and Dr Kev are right.
ie the player’s body is a large conducting object acting as a receiving antenna for electrical fields in the local environment.

If the player’s body is connected to circuit screen, eg via touching the strings that are themselves connected to the guitar screen, then any signal resulting from those electric fields collapses, as it’s dumped to the screen.

However, if the strings etc aren’t adequately connected to the circuit screen, then the player’s body radiates out all the electric field signals that it’s received, and as the pickups / guitar wiring are in close proximity, they will be vulnerable to themselves receiving it.

As ever, I’m careful to avoid the use of the term ‘ground’, as things work just the same whether there’s an actual connection from screen to planet earth or not. eg the player might be using a wireless connection. Apologies if that results in me using somewhat convoluted phrasing sometimes

Actually, there’s a lot of precedent in electronic text books for using the ‘ground’ term somewhat loosely, ‘ground’ and ground symbols are used as if synonymous with circuit common, as well as meaning a connection to planet earth.
eg one or other terminal of a battery becomes the conceptual ‘ground’ circuit common, even on stuff that isn’t mains powered, such as automobiles. So positive ground, negative ground, floating ground, are all common descriptions of various electrical / electronic arrangements, ‘ground’ gets used to describe a nominal circuit common reference point, regardless of whether there’s a connection to the planet.
With training and experience, people become conversant at understanding the particular meaning from the context, but my view is that it’s not ideal at all.
And for non techs (and even some techs!), I think it causes a lot of conflation and confused thinking.
Hence I try to avoid using ‘ground’ or ‘earth’ for anything other than an actual electrical connection to our planet.

Thanks for all the responses.

One of the puzzling things was that I hadn't noticed this hum happening the last time I played the guitar.

So I plugged it into the amp I was using previously, a tweed deluxe kit amp built by a friend, using the same cable.

And it didnt have the hum.

Is it caused by something in amp, either "grounding" or the electrical interference generated by it. The problem amp is a Matchless Lightning 15, brought secondhand recently.

Any thoughts ?