On many vehicles the hot wire to the fuel pump isn't switched on until the engine is turning over, which makes a lot of sense to me. My 94 Toyota used an air intake sensor to switch the fuel pump relay. Now I have a 87 that has a carb.
There are two other ways I've seen this is accomplished. If anyone has done this on a 22R please let me know how.
One way is to put a pressure switch on a oil line like to the oil pressure gauge. I'm guessing you could put a T on that port in the engine
block that serves the gauge and a pressure switch both. . The pressure switch has only one wire to it which is off when there's no pressure.

The other way I've seen it done, on Chevy's, is to add a wire to the hot wire on the distributor that feeds the tachometer,
which only gets power when the engine is turning.
I think in both cases there would be a relay between the power source and the fuel pump. Thats how I'd do it anyway.
I'm going to elecrtric pump because Im getting tired of messing with the leaking gasket on the manual pump. It leaks quite a lot of oil when on the highway
But I'm going to try more sealer today just to see what happens.

 

This might work for what you want.

 

On the carb'ed models, the "Circuit Opening Relay', also known as a fuel pump relay, is switched between the "START" and "RUN" circuits by the oil sender signal. On initial crank, there is no oil pressure and the oil sender switch is closed, which sends full battery power to your in-tank fuel pump, and lights up your "oil" light on the dash. Once the engine starts or you've cranked long enough without a start to build enough oil pressure to open the oil sender switch (oil light goes out), the relay switches to the "RUN" side circuit. That's how the stock setup for the in-tank electric pump was designed to work.

Of course, you could just run an aftermarket electric pump mounted to the frame rail near the tank (see note below), and tep off of both the Start and Run circuits to feed it power, so it can get power in either condition. Only other thing you'd have to do is attach the pump's ground wire to a clean spot on the frame, usually through one of the pump's mounting bolts/screws.
NOTE: It is always best to have an electric fuel pump either in the tank (stock style pump) or as near to the tank as possible, because electric pumps do better at 'pushing' fuel than 'pulling' fuel. Mechanical diaphragm pumps are just the opposite.