Hi Tony,
The throttle linkage for the 'E' code '57 'Bird between the firewall bell crank and the bell crank located between the carburetors is different depending on the transmission used.
The linkage for the automatic looks the most like a mousetrap because of the additional bell crank mounted on the intake manifold near the firewall. The linkage for the T-85 3 speed and the T-85 3 speed with overdrive is significantly simpler because there is no bell crank mounted on the intake manifold by the firewall.
For the 'E' 'Bird, the bell crank mounted on the firewall is unique. It is different from either the firewall bell crank used for 'D' code automatic transmission and that is also different from the firewall bell crank used for 'D' code 3 speed or 3 speed with overdrive transmissions.
A good source for pictures of these linkage set-ups is pages 344, 345, 346, and 347 of the 1949-1959 Ford Car Parts and Accessories Illustration Catalog.
IF the only part you're lacking is the rod between the firewall bell crank and the intake manifold center bell crank (part no. 9747), you are in great shape. The 3 speed connecting piece is simpler than the 3 speed overdrive piece which has a spring mechanism incorporated in it.
I'll email you tomorrow through your Forum account after I've heard back on my inquiry.

Regards,
NoShortcuts
a.k.a. Charlie Brown
near Syracuse, New York