There would be no identified assassin
One of the things that doesn’t seem to have been appreciated about the CON rules is that the process of ousting a leader is totally separate from the leadership election that could follow.
If 15% of Conservative MPs, 47, request that there is a confidence vote in the leader then that would happen without those behind it having to identify themselves and without the move being linked to any of the names that have been floated about at the moment as possible alternatives to Mrs May. All they would do is send letters to the Chairman of the 1922 committee who would institute a secret ballot of MPs once the requisite total of letters had been received.
It could be in the current case that MP backers of more than one potential contender would send letters.
The letters went in about Iain Duncan Smith less than 4 weeks after his 8 minute standing ovation at the 2003 conference. The assumption was ahead of the vote taking place that there would be a contest between Michael Howard and David Davis but the confidence move was not attributed to any of the potential leadership contenders.
As it turned out Davis stood aside in order that leadership continuity could continue without a disruptive leadership election and Howard got the job with effectively a coronation.
My guess is that if TMay’s team sensed that she was in danger of having to face a confidence ballot then she would stand aside on health grounds.