Why can't they? Why is the Death Note not magic?
Because in the canon material it is not magic, people die "without a trace". And you can bring as much from your setting as you want, but you can't change the Death Note setting.
It would also trivialize the challenge for any character that wields magic, because wherever there is magic there's also magic tracking.
If I'm playing a CRPG where 'detect magic item' or something similar is a spell, why would it work on a +3 flaming mace but not on the DN?
The death note is not a magic item in the death note universe. In that universe magic does not even exist, therefore the death note is not a magical item, it's more of an artifact or a natural object
How motivated is my character to stop Kira?
Extremely motivated it's their #1 priority
Dante/Vergil could 100% catch and stop Kira eventually given that the DN would not be able to kill them and, if either of them actually gave a shit would they would be able to track him down using various demon connections/powers/contacts
I can see it but I can also see Light dealing with this in many ways if he can see it coming at least a few days in advance