You still have head gasket or cracked head issue if coolant flows out rad cap opening while engine is cold and idling.
Water pump isn't a "pump", it just circulates coolant, so there is no internal pressure in a cold cooling system, so nothing to push coolant out of radiator, except for cylinder pressure leaking in from bad head gasket or cracked head.
As "air" from a cylinder is pushed in to the head it displaces the coolant in that head, so coolant in rad starts to overflow making room for the new "air" coming in.
Do Glove test to confirm or to take it off the table
Cold engine
Rad cap off, coolant level down at least 1" from top of rad
Overflow hose off and its port on rad plugged, use vacuum cap, gum, putty, hose with bolt in it, ???
Put Latex glove over rad cap opening and seal it with rubber band, you can also use a balloon or even a condom in place of glove.
Disable spark, unplug coil pack or coil, you want a no start
Crank engine over and watch the Glove
If it bounces up and down you have a leak
If it just lays there then you do not, move on
If it bounces then remove 1 spark plug at a time and crank engine
When glove stops bouncing last spark plug removed was from leaking cylinder, put it back in to confirm
You can have more than 1 cylinder leaking, if Glove bounces less then keep going to find other leaking cylinder
Easy to miss a cracked head unless heads are pressure test when off the engine
4.0l OHV heads were prone to cracking between valve seats, if overheated for any reason they will crack, for sure
They don't just crack out of the blue, but if that temp gauge gets above 3/4 then they will
When heated all metals expand, this is normal, heads expand and contract every time you run the engine
Over heating expands head metal more than "normal", 4.0l heads have a weak spot, between valve seats, so crack when they expand too much
Yes the gushing out after a few minutes warm up is the thermostat opening, this is allowing the air that was pumped in from leaking cylinder to get out to radiator
The air is trapped in the top of the head until t-stat opens, the air is what causes the random temp swings as it moves around cooling system, air doesn't transfer heat as well as a liquid so engine gets hot spots around temp sender, then air gets push out of the way and sender cools down again, but same thing is happening all over top of the engine