TCP Timeout for outgoing traffic (LTM is routing the traffic)

I have a 2 servers that reside behind the LTM. There is a pool for these servers but it's not being used in this case. The servers initiate traffic to another part of the network, it seems to use a default tcp idle timeout of 300 seconds. We want the connections to stay open for a day or so. I tried to create a new TCP profile for the pool but it doesn't seem to use that for this outgoing traffic, which makes sense. How would I go about changing the idle timeout just for this server to server communication?

10.105.53.34:3434 - 10.105.2.40:14205 - 10.105.53.34:3434 - 10.105.2.40:14205

TMM 1 Type any Acceleration none Protocol tcp Idle Time 239 Idle Timeout 300 Unit ID 1 Lasthop /Common/vlan_531 00:50:56:87:37:c1 Virtual Path 10.105.2.40:14205 Conn Id 0

                  ClientSide         ServerSide

Client Addr 10.105.53.34:3434 10.105.53.34:3434 Server Addr 10.105.2.40:14205 10.105.2.40:14205 Bits In 1.5K 1.5K Bits Out 1.5K 1.5K Packets In 4 3 Packets Out 3 4