I'll start from the end of your response;
A better auction-system (which I've already suggested) is to allow setting min-price, max-price (and maybe also the difference from current bid), and allow it to be automatically for those who can't attend the bidding.
This is what needs to be done, as there is no reason to give this unfair advantage to users who just have more flexible time.
This game is not about "how your time is flexible".
Summarizing - the auction-system issue needs a "root-solution and improvement".
Regarding the suggestion brought about the half-time auction;
I didn't fully defined it, and maybe something else should happen at this time, but what I'm mainly suggesting is to have something that will bring some small benefit to those who watch a game. Otherwise, as I wrote, there is no reason for this long period of 15 minutes of nothing.
The suggestion:
A player will be randomly peeked from the TL (at setting an auction for that player), and preferably a player of a retired player.
This player will be brought to auction at a game.
As most of the time, the auctioned player will not be one that the users, that are part of the game, will bid and want, that player will return to the TL or even will go to another game as an "half-time auction".
It will give small advantage that users will want to take, as this player will not be open for bidding to all, but just to those two users. This advantage will make users watch the game, or at least the half-time.
In case that player will not be bidded at the first 5 minutes, a new player could be brought to this game.
It is fair for all, as all users will have their own half-time's auction, and what is surely true is that it is more fair than current auction-system (as explained above).
Again, this auctions will not come in replace of the regular TL, but in addition.