Why you shouldn't tie an additional backup to the patient:
1. The patient already has at least 2x connections into the system. We will consider the entire patient in the litter as one "package", and depending on how you look at the bridle system, or if you are using a slightly different setup, then the "package" is connected into the system (both main line and belay line) on anywhere between two to four points based on how the bridle is rigged.
2. If you want to manipulate the orientation of the litter on the fly, having a backup line connected into the patient can hinder that mobility, and you can easily without realizing it load the backup line and this creates pressure & force on the patient because now all the lashing system and the weight of the litter plus any contents inside the litter are pressing on the patient's chest via the external lashing.
If you are still adamant about hooking in a tail of the Double Long Tail to the patient, Don't!!! Instead, consider attaching the tail into the litter frame. This way, assuming the entire bridle system catastrophically fails the force will be transmitted into the litter and not the patient. Also if you're going this route, you do not want any slack in that backup line should the bridle system fail, because otherwise you introduce a shock force. So it then becomes one more additional thing that needs to be tended via a Prusik.