That motor is thermostatically controlled. So, if the water is cool, or at start up, there will be nothing more than a mist coming from the rear of the motor. When the thermostat says the water is hot enough, it opens, and the flow will increase, until it senses cooler water, then will close again, and again you will have nothing more than a mist. It will continue to do this, opening and closing, while you run.
Also, you need the water lever quite high when testing in a barrel. Almost to a couple inches below the exhaust relief hole you mentioned. The pump is NOT self priming, so it needs to be fully submerged to work properly.
Never remove the thermostat, nor the spring/nylon combo. If you do, exhaust gas could work its way back down to the water pump, rendering it useless. They pump water great, air/exhaust, not so great. Keep the whole t stat assembly in, and in good shape.