Yes one pump, won't be a relay since it has to be running to have driver's side spray. Yes it has to be a clog or rotted line and it's leaking before it gets there.
I haven't taken this apart on mine and you didn't mention which engine (does it matter?) but the basic procedure is just unbolt the tank, assuming you can't get the lines off without doing so since they're on the bottom, or at least not easily without possibly damaging one. Check the tank for gunk. In some areas people have fungus growing inside. I'd have thought the alcohol in washer fluid would prevent that but apparently not. I'm just saying no point in clearing a clog in the lines but not the tank too, if gunk in the tank is just going to clog it again.
At that point I would be lazy and try putting compressed air through the line, instead of first disconnecting it from the windshield nozzle to see of the hose itself is free flowing, but you might end up having to do that anyway. Well, free flowing also means you're getting air out the nozzle, not a leak between the two points. I don't know if too high an air pressure might rupture the hose or blow it off the nozzle so I'd start low pressure. If it's mineral deposits clogging the nozzle then a soak in vinegar might dissolve it... after a while, the process sped up by warming it and occasional agitation.
