Having a bootable external drive is not the same as having a bootable backup external drive.
If you have just removed your original drive and slapped it into an external enclosure and are now able to boot from that drive without using SD! or CCC and wish to add a TM backup to that partition - should be able to do that - although I would not recommend it.
Yes, in order to use TM, you have to tell it what drive/partition, you want it to use. TM does not delete any other data on the drive/partition and has the ability to co-exist with other data but it is not a bootable backup.
If you are going to use SD! or CCC to create and maintain a bootable "backup", each of those apps create an identical clone of your internal drive - adding what is missing on the external and deleting what is not on the internal drive. Both of these will delete any TM backup or any other data you have added that does not exist on your internal drive. This is my personal first choice for a backup. Yes, in this scenario, you will need to partition the drive and use one partition for the bootable backup and the other for TM.