Help Identifying this Sound Effect

Sorry I don't hear any "sizzle" but I do hear a second part come in that's sort of like an organ but I think is just a guitar part layered in there. It could be a synth. 
 
Yes I think it is as you can hear a definite,, what ever that is when keyboard players wipe across the keys,, in the start of the solo/ 
 
Keyboardist Geoff Nicholls, who was a session keyboard player during the recording of this album,

Going through some of the TH3 presets (Full version), some of the classic rock presets have this quality.
 
What they seem to have in common is boosting the treble on the amp to the point of it sounding really tinny and nasty, but then using a cab/mic combination that then takes most - but not all - of it away. So basically the cab is acting like an imperfect low pass filter.
 

It could be a noise reduction artifact which was the Bane of tape based recording in those day's. 
Especially this happened in the upper frequencies. To mask the tape hiss Dobly or DBX, as example, would mess around with processing the upper frequency where the hiss was. I totally forget how it works because there's no point in remembering anymore.   Go read up on Tape hiss and noise reduction..  It will start all of us old goons off yelling at you for wanting to bring back what we don't miss about using tape :) 
Like the guy who wanted to figure out how to add record scratching to his recording,,,, geeeze///

Don't know how to get a hold of Martin Birch, BUT...I've been using Wave's Aphex Aural Exciter plugin a lot lately, and that COULD be it.  Don't actually play any metal-ish stuff, but the effect sounds a bit like you describe and suits me for both the acoustic and electric guitar parts I do (in moderation).  Waves offers a free trial on their plugins, you may want to give it a spin...

I've always love Tony's sound. Listen to the album Paranoid and you will hear amazing solos like in War Pigs. Dual solos panned right/left. But the Sound of his pick ups in the SG with the combination of a Marshall. It just doesn't get any better really.

Matron Landslide
Except for the fact that he used Laney amps for the recording.

Obviously not for the album the OP is asking about.
The link in the OP is a song from the album "Heaven and hell".
 
Marshall Super Lead 1959
This amp was modified by John “Dawk” Stillwell, who designed a new circuit for it that included an extra tube and a master gain control. The amp was used on Heaven and Hell and Mob Rules albums""

After the breakdown on Neon knights I do hear (I believe) it sounds like a keyboard.
But its not at 1:50 its almost 2:00.
 
If you want to hear some great tones, check out this guy on You tube.
He is one/if not my favorite tubers.
 

 
I personally love SG and Les Paul's (the older ones). But my personal favorite guitar is my 2003 MIA Fender Strat with one Humbucker in the bridge. I don't like the twang of the Strats (The 3 single coils) So I pulled those out and put in a custom made Seymour Duncan from the 80's.
 
It just takes a while to find the right combination of Guitar/Amp. For me it was the Strat and a modded JCA Jet City 20.
I have Marshalls, Vox, Peavey 6505 and a slew of other amps including multiple cabinets with over 20 different speakers I pop in out of the cabs. Right now my fav is the Soldano 2x12 with a Vintage 30 and a Creamback.
But the JCA 20 with the Friedman mod just breaks up fast at lower volumes.

Cactus Music
It could be a noise reduction artifact which was the Bane of tape based recording in those day's. 
Especially this happened in the upper frequencies. To mask the tape hiss Dobly or DBX, as example, would mess around with processing the upper frequency where the hiss was. I totally forget how it works because there's no point in remembering anymore.   Go read up on Tape hiss and noise reduction..  It will start all of us old goons off yelling at you for wanting to bring back what we don't miss about using tape :) 
Like the guy who wanted to figure out how to add record scratching to his recording,,,, geeeze///

You may onto something here - Dolby / DBX noise reduction circuits did a exaggerated high frequency emphasis when encoding and a reversed DE-emphasis upon decoding. There were scenarios where these could be switched on and off or bypassed. I remember wishing I could keep the emphasis on occasion but just dial it back a bit.

Hmmm, you don't mean the doubling sound? Kind of chorusy? There is a second guitar there. It's double tracked but has a different sound and is lower in the mix and panned about 50% left. Apart from that, there's a bit of phaser and the treble has been boosted on the saturating valves/tubes and there's a short reverb, maybe amp room ambiance. Then when the solo comes in there's some Hammond with it. I'm not hearing anything more special than that.

It's two tracks with typical stereo widening during mix.  But that has nothing to do with the effect I'm referring to.  Listen very closely, it tricks the ears and is very easy to miss.  It requires decent monitors with good top end. There is something being applied that has nothing to do with the native signal coming into the board.   There's an entire frequency/harmonic spectrum happening in the upper layers that is not coming from a guitar amp or typical effect.  

@SonicExplorer

I think what your refering to is the side effect of the preamp/OD boost.

Maybe a bit, to me that song sounds more natural though, could be simply chorus and some EQ, along with widening.    The stuff I'm referring to is not just chorus and EQ, there's something else happening, you can tell by the un-natural frequency carvings and harmonics in the upper registers.  Back in the day, typically the drums and bass were tracked (sometimes with scratch guitars) and then guitars rigs were carefully mic'ed to accommodate the song, with tweaks to the EQ on tracks coming in.  Then in mix the guitars were already 90% there, they usually needed just another small nudge here or there on the track EQ.  Granted, yes, there were things such as an outboard parametric EQ or a 31 band EQ, but those were usually not used for guitars.  Point being, today with a DAW we can do all kinds of frequency carving, notching, etc - many many bands.  This entire approach was typically NOT utilized back in the day, rather as I explained.  So while today it is theoretically possible to get an EQ to help create the sounds I'm referring to, it is definitely not what is heard on the recordings I'm referring to. Especially given the same thing is heard on different releases with different artists and producers.  No way is that some fancy, complex analog EQ carving coincidence.   And not just attributed to reverb or modulus effect, or multi-track widening, rather something additional is being utilized.   Once your ears latch onto it, you'll hear it in various songs from the early 80's.   And then you can't ever un-hear it.  

Hi. A slow flanger/phaser, maybe?

JR