Are you absolutely sure it's not low?  The symproms are correct for
marginally low coolant, comes on when cold and goes out when the coolant
heats up and expands in volume enough to put the light out.  Always happened
that way on my Aurora.  Try adding a litre of coolant and see what it does.
No relationship to pressure. Too many possibilities to guess on the check
engine light, but more likely to be a temp rwlated sensor, air intake temp,
ambient temp, coolant temp etc.  You need to retrieve the trouble codes.
Steve