Congrats on getting your Bendix up and running! Do you happen to know if the coil on the hot side of the valve is good? I'd first check to make sure the coil isn't open, using a multimeter.
If the coil checks out to be good, you could try wiring 120v straight to the coil, separate from the machine harness/circuits, just to make sure the diaphragm is operating. But yeah, otherwise the thermostatic element within the valve could be stuck on cold. This would require disassembling the valve, cleaning all the parts - removing scale and lime build out on the element. I'm always a bit leery of disrupting the diaphragms on these early valves as replacements are incredibly difficult to find and are prone to leaking, post assembly.
Next time you look in the mirror know that you're lookin' at the person who will be rebuilding the timer

. All of the timer rebuilders have closed up shop or have changed their business model and no longer rebuild laundry related timers.
Thankfully the contact block portion of the timers rarely have issues, but the black Ingraham timer motors on the escapement are usually the culprit. A few collectors have had success taking the cover off the gear side of the motor and have gotten them to start running again by lubricating the drive side of the motor. But often the windings on these will blow open from age. Check for continuity on the motor before going through the effort of getting the drive working. If the windings are open you'll need to find a replacement motor. Often, the later gray style motors can be used from 1955-ish thru late 60's and later Mallory timers. Frigidaire and Maytag timers can be a good source but you'd need to verify the gear size and tooth counts are the same, and work on modifying the bracket that holds the motor in place (I've found that flipping the original black motor bracket and bending the ears usually works fine).
Ben