Which EFI are you running? Ford or aftermarket?
This won't necessarily tell us anything about what's going on specifically, but gives you the pressure readings you're looking for.
While that 36 is just adequate for running a earlier Ford EFI (EEC-IV?), it's beneath the lower level of normal which is around 40-49 if I remember.
If you're running later Explorer (EEC-V?) then yes, it's more like 55-60 or something like that. But the others will know that, so don't go by my memory.
Some aftermarket TBI units use still more. So even if you were running a steady 36 it would be below par. Since it's not even consistently pressurizing though, you obviously have something wrong with either the fuel system or whatever is controlling it.
Sounds almost like a bad wire or connection to the pump. But I suppose it could be a bad pump on it's way out too.
What pump, where is it located, and how long has it been in service?
Single pump, or a low-high setup?
Johnny-5 needs more input...
Paul