Do not run it out of water unless you disconnect the pump.

Just towing, you will get a lot of dirt in between the impeller and wear ring.  Running it with the abrasive dirt between the two will accelerate wear and degrade performance.

Even if you do run on the hose and manage to flush the debris out from between the impeller and wear ring, having water pressurized between the two will actually lubricate the wear surfaces.  This is just not possible on the hose.

Lastly, the packings are lubricated by water leaking into the boat at a rate of one drop every ten seconds.  This water comes from the suction housing being pressurized by the forward motion of the boat.  There is no way to replicate this with a garden hose.  Running the pump dry for more than a few seconds will burn and glaze the rope seals and also cause damage to the shaft where these seals ride.  Once the packings no longer seal, not only will you have water leaking, but they will also leak air, when the suction housing is under vacuum, causing cavitation to the impeller and bowl.   This usually occurs on the hit.

Jet pumps are pretty bulletproof if you take care of them.

If you must start it on the ramp, it is good practice (even if you don't start it on the ramp) to open the reverse bucket, aggressively back the boat into the water, then pull forward to flush the pump of road grime.  I do this twice.  Then you can start it for a few seconds, just to make sure it starts.

I would tune on the water because the pump will slightly load the engine.  You won't get that on the trailer.

While on the topic of what not to do to your jet pump:  Don't drive on/off the beach.  When shoving off, walk the boat out to waist deep water.  Bounce the stern a few times to flush rocks and sand out of the pump before starting the engine.  Keep in mind that the pump will suck sand off the bottom from 3-feet away.

Welcome to jet boating.

Cheers,

Joe