Please see attached diagram for more details.
You have a connection to vendor/business partner. You have two connections to this business partner. You are runing EIGRP on your internal network and with your routers and core switches. You don't know and don't care what IGP's the vendor is running. They are most likely doing statics. The vendor has two circuits from their routers to their network. If one of the vendors circuits goes down their equipment will failover to using their seconday circuit and equipment.
NOW the BIG question:
How can you configure your company primary router to notice when the vendor primary fails over and instruct your secondary router to take over as the primary path to the vendor network. Your company routers are using HSRP over a L2 link and the primary has static routes pointing to the failover ASA HSRP address of the Vendors ASAs.
I think you will have to do some sort of interface tracking, but not 100% sure.