OK, this has got me baffled.

Guitar is a 1990s ES-135 with P100 pickups. That's the stacked parallel-wired hum-buckers that were Gibson's first attempt at quieting a P90. They're nothing like as bad as many opinions claim, apart from having a very low output.

Anyway, it's developed a loud buzz in all switch positions unless I habe contact with the metalwork or strings. Which is a pain as I use it for slide and use a glass one which doesn't shut up the buzz. Which is loud enough to be heard all the time and louder than the notes. The pitch of the buzz changes depending on where I put my hand on the fingerboard, almost like I'm tuning a radio. Happens in all three switch positions and changes tone depending on the switch position.

Now, I know what you're thinking. The string earth between bridge and pots/jack socket has got itself disconnected. No it hasn't, I checked that first with a meter and it seems fine, resistance is less than two ohms. I've also dug the switch out and it seems OK, though I cleaned it anyway to be sure.

What hair I have left is in danger of being torn out.

Any ideas anyone? Because right now it's in serious danger of being traded in against something electric and hollow without "Gibson" written on it.

RF interference from a neighbors (new) device?

I would still try reheating the bridge ground connections to a full melt.  They may look OK visually, but it should be zero ohms for that short (hehe) run.
 
You might have a cracked solder joint from jumping off of speaker stacks with it on stage.

Get a digital multi-meter. Connect a cable to the guitar and measure the resistance of the neck, middle and bridge positions. The neck and bridge should be close and the middle should be about half that reading. If you see an odd reading it may indicate that one of the 4 coils in the 2 pickups has died or has a bad connection.

I should have mentioned the ***** thing is much noisier than my Telecasters....

I was wondering about a bad pickup, but if that's the case then I'd expect the other pickup to be fine, so the buzz would be on the affected pickup and "middle" switch position while the good pickup would be fine.

The symptoms have come on very gradually over the last couple of weeks. Originally it sounded like the switch was vibrating and making intermittent contact on the neck pickup with the interference breaking through as notes died. At the beginning I wasn't sure it wasn't the amp being a bit 'spitty' as it dropped out of overdrive as the note decayed. Now it's everywhere.

I've a nasty feeling it might be a broken or cracked solder joint somewhere. Hopefully it's the switch, because getting the pots out of an ES is not a job I look forward to. Luckily this 135 at least has the correct big holes in the (balsa) centre blocks where the pickups sit to feed the electrics through.

I've never had need to take the pots out of this guitar, for which I'm grateful. Then again it hasn't been played much. It's good for John Lee Hooker and R L Burnside style modal blues but is a strange thing to play and lots of things about the design are sub-optimal. I've had a love/hate relationship with it for years. On the plus side I paid less than half list price for it new.

Fender in the CBS years had a bad reputation, but Gibson have made some howlers in their time as well. It's on its sixth set of knobs, they kept cracking, often as they were first fitted on the splines. Until Gibson re-jigged their knobs a few years ago to have a slightly wider hole with thinner splines that actually fit Gibson potentiometer shafts that is.

Anyway, thanks for the suggestions, I'll investigate further. I thought after 40+ years playing and 30 doing setups and electrical repairs for people I'd seen just about every way a basic traditional Fender or Gibson has to go wrong in strange ways. Clearly I hadn't.

Something, somewhere is no longer grounded properly. 
 
First make absolutely sure it's not the amp. You really, really don't want to be the path to ground.

BobF
I would still try reheating the bridge ground connections to a full melt.  They may look OK visually, but it should be zero ohms for that short (hehe) run.
 
You might have a cracked solder joint from jumping off of speaker stacks with it on stage.

I believe Bob is right on it. My friend and I have talked about how it is the most frequent wiring screw up on electrics. the bottom of the bridge is either chrome or just bare steel and the gound is often just a blob on a wire you can pull off. And just cuz it's there doesn't mean it's doing the job. You describe a ground problem andf that's it even if it looks okay. Clean the bridge with some rubbing alcohol  and tin the end of the wire and the spot and solder it back on. Clean is the big word on this.

It sounds as if you have a great guitar ....I hope you sort it out and fix the problem ...
 
Kenny

The amps are most definitely fine.

It'll be at least the end of the week before I can dig into the thing properly.

The bridge earth as I remember it is just a wire trapped between the Tunomatic post bush and the laminated maple top. I had a try at getting a soldering iron to it a few years ago but there isn't enough spare length in it to get the wire clear enough if the lacquer to want to get a hot iron anywhere near it. Just soldering an extension length on to the existing wire is asking for finish damage.

Well, if in the end I have to dig the pots out it'll give me the excuse to finally get around to replacing the 300K linear taper volume pots with 470 or 500K and maybe swap the caps as well. It could really do with a bit more top and output. I've seen a few people on the web claiming that P100s are really hot pickups. Believe me, they're not. Similar to a vintage Strat maybe, certainly less output than a vintage-output Tele bridge or neck pickup and with very uneven string response as well. My '61 Les-Paul-SG Jr's single P90 is much louder and has much more 'cut', but talk about hum....

Like I said Kenny, I've a love/hate relationship with the 135. It's a design (well, reissue version of a much older guitar also called the ES-135) that almost works but in original form like mine has it's peculiarities. As well as Gibson's least favoured pickup of all time it has a trapeze tailpiece that makes the tail to tuner length so long some brands of strings won't fit - the wound section isn't long enough to cover the distance and restringing is slow and fiddly. It's heavy. Very heavy. It squeals and feedbacks at quite low gain courtesy of unpotted pickups and a centre-block made of balsa.

By the time the 135 had been on the market a few years Gibson had redone it with humbuckers, Nashville/TOM bridge and stop-tail and a mahogany centre block. Making it much like a heavier, deeper 335 soundalike. It finally became the ES-137 and now seems to have dropped off the Gibson catalogue.

I've been tempted to trade it a few times over the years, only people keep telling me it sounds really good. I think they're just overwhelmed by the redness and bigness of the thing,

i you love the way that guitar plays...
 
and something has gone wrong with the electronics,
 
if it were me, i'd do some research and replace the pickups with an aftermarket.
 
there are SO MANY GOOD PICKUPS out there now,
it's very likely that every penny you would spend would be worth it.