I swear you must've been reading my mind.
I was thinking that he may potentially reopen his recruitment if their HC, who just so happens to be on the hot-seat, gets fired. I don't know why he chose not to sign his NLI, but I have a feeling that may be a reason why.
Though, if (and probably when) Brooks pulls the trigger, we'll be pretty crowded. So even if Tilmon does decommit, that's still a lot to work with and he may consider other desintations.
Still, all just speculation until it happens.