Looks like no responses yet so I'll give this a whirl (new here, been a Vette owner for about 2 years mostly active at CF).
So it sounds like a couple things could be going on. You shouldn't get a leak out of the hoses at all, so if that is happening, they may just need replacing (they're 10 years old now). If the leak is out of the nozzles, then you might have backflow problems. You should check that the pump outlet is unobstructed. Heat expansion + no backflow could explain why this only happens on drives where the car warms up.
But let's suppose the pump is running intermittently on its own. It is not the pump; I just checked the service manual (2000 but close enough) and this is a 2-wire connection, so it is switched with full power externally and therefore cannot run on its own. You have either a bad relay, a bad switch, or a bad wire.
I would say get the car to where it is doing it (warmed up). Get yourself a test lead or a multimeter and unplug the pump plug. Look for signs of continuity or voltage. These should be open & no flow. If you see voltage, you know the hunt is on to find a short. I haven't looked through the manuals for the wiring diagrams but there's probably a relay, so this could be a cheap fix. Electrical debugging is a dark art but generally I like to work the switched-to-switch for shorts and the other way for opens, testing continuity the whole way.
HTH,
Dom