high frequency intermittent noise

I'm virtually 100% certain that's cell phone signal interference. That is exactly what an LTE signal sounds like when it's being picked up by an unshielded/under-shielded wire in the signal path. I doubt it's being picked up through the power lines, but I can't be curtain. If it was, you'd hear it through your TV and computer. I'd be looking at interconnects. 

LTE is an evolution of GSM. It uses a combination of TDMA and FDMA. The various high speed pulses are the individual data packets broadcast in the data windows. Their intensity is the product of the frequency their transmitted on and how well tuned the antenna is to them. 
To be honest I'm surprised an antenna across a street can do this. Another possibility is that somebody very near by has a picocell or a femtocell installation in their unit. That's common in larger cities. I wouldn't be surprised if unshielded tubes picked this up. Something somewhere needs more shielding and I'd be focusing on that as much as possible. I'd be tempted to build a Faraday cage and put gear inside it to see what happens. 

AM is WAY too low in frequency. Cell phones broadcast in the 700 to 2100 MHz range. Not every tower serves every cell phone user. If it’s not a microcell of some sort it may me an LTE based hotspot. Whatever the source, that IS a TDMA signal pattern. It’s not WiFi because WiFi uses a variation of frequency division for point access. Bluetooth uses a frequency hopping scheme and would only be audible briefly.

Got me. I know that sound though. My cable in my car is unshielded and if I leave my phone on it that's exactly what I get. Same thing if I put it near the interconnects on my stereo at home. Not many things use TDMA because it requires extremely accurate clocks to compensate for the speed of light so that the full packet window is utilized. That low level high pitched hum in the background is the timing reference. The major benefit of TDMA schemes is power and bandwidth conservation. You don't really need that with short distance, low bandwidth applications. There's cheaper ways to do it. If I was having this issue I'd be playing YouTube videos on my phone while moving it around all over the system. If something feet away is causing the problem, something inches away will definitely be heard. If a cell phone broadcasting near by can't replicate the problem then I'd start looking to something outside the area. Whatever is picking it up will be aggravated by a cell signal. I can't think of any other kind of signal that could be. 

As sure as I am that it's cell phone noise, I'm almost certain it's not that tower. That tower is serving dozens or hundreds of clients at any one time. If it was the tower it would be practically constant. Something in the building is the source, and it's close. Last night I played around. I got my phone steaming videos last night and put it INSIDE my F5 right up against the left amp board. I could barely hear it. It was strongest when I placed the phone on top of the toroidal and right next to the power cord. Even then I had to be inches from the speaker. 

I would assume he could do what I've done. If there's some point of weakness that might sniff it out. Referring to Atmasphere's post about resistors, the one thing an F5 has is resistors. No caps on the amps at all. Just 8 big filters in the PS. That may explain it's rejection when placed near the amps. I accidentally neglected to put a CL60 on the ground though. That may explain why I get it through the power supply. 

You may be into something with the building system. Some security systems use cell connections to avoid the possibility of wires getting cut or just running more wires period. 

Might mu metal be more effective than aluminum foil? 

I'm not sure where this 700-800 MHz figure came from, but LTE bands usually operate up in the 1.7 - 2.4 GHz region. 

@atmasphere 
Nelson is good indeed. Maybe I shouldn't be surprised the F5 is resistant to that kind of interference. It's all resistors and it's designed to shrug off MHz range ringing because of it's crazy wide bandwidth.