I just looked at my Aerostar: a 1997 4.0 liter Extended Window van; Yours is a 3.0.

that connector shown in your picture is not in my engine, zero, nada. I looked everywhere with a bright lamp, no wonder I couldn't figure it out.

does your van have air conditioning? Is it a Cargo van?

what your second picture looks like, is that the Temp Sender for the Dash Gauge is mounted to that part where the hose is leaking, that's the only similarity I can see. (the temp sender). the Temp Sender in my engine is mounted further back, not where yours is.

But repairing the leaking hose is easy: loosen the clamp, remove the hose by twisting it left to right, (you might have to tear it off if it glued itself to the nipple);

do as xlt4wd90 said, cut an inch or more from the hose and reinstall it on the nipple; (short of replacing the entire hose which might be the better way to go). Using some type of sealer on the nipple would help eliminate any future leakage. I use Indian Shellac when replacing coolant hoses.

PERMATEX 20539 INDIAN HEAD GASKET SEALER $2.95 BUY ONLINE

get it at any autoparts store and while you're there, you might as well get a new hose. Napa or Autozone should have the new hose.

clean the nipple with sandpaper or sacrifice your wife's emery nail file if no sandpaper,

apply a thin coat of Indian Shellac to both the nipple and the inside of the hose, (just to the first inch or so of the hose's inside wall, easy does it), do not overtighten the hose clamp at the nipple, just tighten enough so that the rubber is not deformed by overtightening. Let dry before running engine and then run engine and observe for any leaking, tighten a little more if it leaks.

Piece of cake and celebrate!