Sale 1: https://backpack.tf/profiles/76561198087172601#!/compare/1494460800/1494547200 - Use on the Taunt, i guess.

Sale 2: https://backpack.tf/profiles/76561198087172601#!/compare/1494633600/1494720000 - Sensation.

Sale 3: https://backpack.tf/profiles/76561198216133209#!/compare/1495756800/1495843200 - Vive.

Sale 4: https://backpack.tf/profiles/76561198208062409#!/compare/1496275200/1496361600

Sold for a Clean Orbiting Fire Brown Bomber (28 keys) + 3 keys in adds

28 + 3 = 31

ADDITIONAL PROOF BY BIRDY:

https://marketplace.tf/items/30307;5;u60/Dead%20Presidents%20Neckwear%20Headwear - ~26 key sale from early May

All sellers on bp.tf are below 31 keys, although it isn't clear how long they've been up. Judging by who the sellers are and how long they've owned the Neckwear, it looks like they've likely been re-listing, but I can't confirm this or at what prices if so.

Additional by Marty:

27 still unsold, now for over a month. An additional seller for ~26 on MP as well: https://marketplace.tf/items/30307;5;u60/Dead%20Presidents%20Neckwear%20Headwear

So it turns out this is still too high. This should be 26 flat.

26 it is!