Here's why:
* 700R4 Transmission Needs Vacuum Modulation: The 700R4 transmission relies on vacuum pressure to control shift points and firmness. The vacuum signal is used by the transmission's TV (throttle valve) cable and modulator valve to determine the appropriate shift points based on throttle position and engine load. Without vacuum, the transmission will likely shift erratically, harshly, or even fail to shift correctly.
* Other Vacuum Systems: Even beyond the transmission, your 1956 truck likely uses vacuum for other things, such as power brakes or the distributor advance. This is critical for safe and proper operation of the truck.
* Adaptation Necessary: While the engine and transmission *themselves* might fit physically (with the right mounts), considerable adaptation would be needed. This includes:
* Transmission Mount: Fabricating or sourcing a new transmission mount.
* Driveshaft: A custom driveshaft would be required to match the transmission output to the rear axle.
* Vacuum Supply: You'll need to create a vacuum source, possibly from the intake manifold. It may involve adding a vacuum port if it doesn't exist.
* Wiring and Controls: The 700R4 will need a proper electrical connection, possibly requiring modification to the truck's wiring harness.
* Cooling: Adequate transmission cooling is crucial.
In short: While mechanically feasible with significant modification, the lack of vacuum lines makes this a very challenging, potentially dangerous, and very expensive project. It's highly unlikely to work properly without addressing the vacuum issue and other necessary adaptations. You'd be far better off choosing a transmission that's more compatible with a classic truck lacking a comprehensive vacuum system. A more appropriate choice might be a Powerglide or a later, simpler automatic transmission that doesn't rely so heavily on vacuum.