Check your power source. Dirty power will do that. Route all devices connected in any way to a central point and plug into different points around the building to confirm if possible (try to find different phases). A decent power conditioner might help, or an isolating transformer will do the trick. Some equipment may need to be star ground.

I am using Furman PL plus DMC conditioners. I'd be more suspicious of power if the clicks weren't only occurring on the 2 lav strips and of course I have tried using other strips, but with same result. When the clicks occur they are so consistent that it reminds me of something like an electrical relay switch, but I can't figure out how it's there. I can't predict when a click will happen and I haven't been able to replicate it. The recording of it I posted is a rare occasion when the click happened in a moment between script segments.

Yeap, things like this are frustrating to track sometimes. Im suggesting this as its exsactly what happened to me once when I had my old analog console.
In the end I needed to star ground everything in my studio and place an isolating transformer between the main incoming power source. I believe it was a problem caused with older, high drain equipment and my newer digital gear. Im not in a commercial building here either, so I just have standard 'dirty' power coming in.
Could be any number of issues causing your clicks, but power would certianly be top of my suspects.

If you simply remove the 77's and replace them with a different mic (anything, say a Shure SM58) does the ticking go away?
This ticking, is it showing up on a digital recording ? Analog...both?
Do you have an appliance like a refrigerator or airconditioner using the electrical service?

I'd agree with the majority here and go for power supply. It may even be traffic signals outside but in close proximity. And here's another thing to try. If you have a TV or VHF receiving Antenna strapped to your roof, especially if it goes via a signal booster, which is connected to the domestic power supply, remove it.

It could be that an insect has crawled into your ear though.

MS

As I said, I am unable to replicate the clicks on demand, but I haven't been able to detect the clicks on any other non phantom powered mics on the same lines. We have used other ECM lavs, and countryman E6s and noticed the clicks. The other challenge is that troubleshooting is especially hard in terms of duplicating the recording environment is difficult because the crew and is only available at scheduled recording times and during that time, there's no opportunity for experimentation with crew and talent and all gear active. I have a Neumann TLM103 connected to the same board which is not giving me clicks, the key difference being that it is in a vocal booth and not the studio. The only thing distinctly unique thing about the mic lines in question is that these two are my longest audio runs, but good canare cable and ends I put on myself and when swapped for other non custom XLRs I have the same problem.

There's no fridge or appliance or non gear fan in the vicinity except for 1 teleprompter PC, but it does not share power with any gear. My singular suspicion as I think about it now is that I didn't supervise the routing of the snake and it's possible that it may be near some power, however there is no problem in any other Tx/Rx on the snake - then again, almost all other channels are occupied by line level signals... hmmm...

The recording is pretty simple - all analog to decks but all digital recording Mains (through snake to drawmer da6) to two HVR 1500s - one deck send HDSDI with enbedded AES to Kona 3 for MAC capture. Clicks present on tape and on capture. Same board, sub out direct to Marantz hard drive recorder - not through snake, clicks present there too.

Power was not what I have been focused on because I figured I have heard every kind of audio problem related directly to power, but I have never encountered anything like this before, but I mentioned I don't call myself an audio tech first and foremost, so I was hoping some noise boys would have more ideas.

It's one of the most basic things in my whole build but I am still getting beaten by it and it's driving me crazy.

Does the snake route to any kind of patchbay or multbox? More importantly, do the lines to the vocal booth route in that manner? I used to have problems with a noise like that on Shure SM81's that were running down a snake in a church. The installer had routed a group of the XLR stage inputs to a multbox in the machine room, for future splitting options. A bad connection in the loom at the multbox was causing the phantom power to be interrupted sporadically, causing a very noticeable tick like you've described...moving the mics to another set of lines NOT routed to the box fixed the problem.
Then we resoldered the loom, and Voila! Just a thought...

I would have thought power capacitance (cross talk from power lines to audio lines) would not create random clicks. You would get humm. As another thought, are you drawing too much power? Its a long shot, but if you're right on the verge of pulling max currency from a circut, weird things like this might happen? Some of that old analog gear might be spiking when it draws voltage, causing the digi stuff to play up?!

Worst file sharing site I've seen to date.

Anyway, let me float another idea out there.... do any of the people involved in the production have smartphones in their pockets? iPhones, and the like, radiate all kinds of garbage whether they're physically being used at the moment or not. There are phone specific pulses that transmit back and forth between the phone and the tower almost constantly to maintain service and ping for new messages etc. regardless of whether the user is currently texting, talking, or web-browsing with it. Not to mention the relentless search for wi-fi etc.

Maybe not a factor, but worth consideration. It would be easy enough to test.

Best of luck.