Issue:
From my testing with attacking mounts such as golem and beast mount, I can say that once the mount died, the rat itself will begin to attack on its own. The problem is that now this rat only has like 8hp and would definately die.
Solution:
Have the rat to not attack anything without its mount, only when another mount spawned, then it may proceed.
With the exception of other passive mount such as chicken and strider, since these do not attack.

Added in 5e55839