I go through this after my '37 goes undriven for many months too. The following is the process a buddy offered and I have used. Others may be able to offer help, perhaps better.
Check for brake fluid leaks:
Was or is there any indication of brake fluid below the brake cylinder or on the tire or ground below where the truck has been parked?
Is the master cylinder brake fluid level where it should be? If only low, add fluid.
If the answers are Yes, then try this. (If the master cylinder is dry the process gets more involved.)
Remove the brake drum and check for any type of contamination. If there is any, clean as needed and replace the drum. Fine grit sand paper on the drum and pads has been used. Then retest.
Chances are the leaking brake cylinder will need repair or replacement. But, the above can buy some time. I've got the repair on the '37 maintenance list. As I understand it the rubber used in reproduction cylinders and repair kits is prone to go bad sooner than later.
I don't know what a J-4707 tool is, but my guess is an alternative is and has been used successfully by many.
Good luck.
