yep. Clean it very well. Simple green, or Spray Nine etc, strong spray soap, get it everywhere, then hose it off really well, let it dry or help it dry with compressed air, fans etc.
Once its dry, start the car and watch it. you have no water pump like this unless you hook up some belts, but if its cold it will be fine as you say it only takes a min or so to get the leak.
I personally don't like the frost plug you have in for blocking off the front bshaft. It doesn't look fully seated. That and those iffy hardware store bolts (3 of them below the frost plug). Use good bolts in this area.
None of the tensioner, pulley etc bolts need sealant, so its not from that.
If one of the seals is gone that badly, detension and remove the timing belt and carefully inspect the shaft it seals for any play at all. Usually a seal, unless it falls out(check that too) a seal will normally just make a mess, but slowly. but if the bearing or shaft is badly worn, the seal will puke like crazy. With tension on the Tbelt, you won't be able to detect the play.