"There is no mention why the other “conservative” justices voted for the ruling."
I suspect the reason is Kavanaugh and Comey Barrett are scared for their lives and the lives of their families. Death threats, assassination attempts, protests outside their homes are having the effect the left intended.
These 2 judges need to learn the lesson the rest of us learnt in our early years of schooling. If you do not stand up to bullies, the beatings will continue.
As long as they keep folding and not publishing their reasoning, the left is going to continue to believe their tactics are working and will keep ramping up their efforts.