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UPDATE: With the arrival of Season 3, some information in this video has changed. Here are my current findings:
• 1:31 Using a voice line now increments the mute timer by 5 seconds.
• 1:40 The mute threshold is now 10 seconds.
• The above information means the new optimal spam cycle is [use 3 voice lines, wait 15 seconds, repeat]
• 1:52 Using a voice line while muted will no longer extend the mute timer (in most circumstances; if you constantly spam the voice line key, a small delay is added).
• 2:22 The mute ramp-up now occurs at around 18 voice lines. The exact scaling is still unknown since it would take an inordinately long time to figure out, sorry.

If you want to verify these findings or experiment further, here is my script:
Workshop Code: 5Z3V9F
overpy script: https://pastebin.com/raw/0RLX5jin

TIMESTAMPS:
• 0:00 Introduction
• 0:57 Muting Mechanics
• 3:30 The Future

REFERENCES:
• blizz_winter's comment -   / j4xc2v4  
• TF2 Crab Spy -    • TF2 Crab Spy  

MUSIC:
• Super Monkey Ball - Monkey Target

ME:
• Twitch -   / marblr  
• Twitter -   / marblrr  

Footage captured on game versions 2.2.1.1.109168 and 2.2.1.1.109670