ECT sensor has 2 wires, thats the one computer uses to set Choke Mode(Open Loop) or Run in Closed Loop, warmed up engine.
No it won't hurt anything to leave ECT unhooked but Computer will run engine a bit Richer.
MAP(intake manifold pressure) sensor may be the issue however, since you are at 10,000ft elevation.
When you first turn on the key the MAP sensor will establish air pressure at trucks location, at 10,000ft pressure would be lower so computer would recognize this and lean out the air fuel mix to match.
One of the draw backs of MAP systems(speed density) was that if you started engine at sea level then drove up into the mountains engine could start running rough, or visa versa(drive down from the mountains), but simple shutting key off and turning it back on would reset Starting Pressure for current elevation, i.e. stop for gas and truck runs better afterward.
MAF(mass air flow) system didn't have that problem, lighter air/less pressure is compensated for by hot wire cooling less so less fuel is added, same as warmer air.
I would check the MAP sensor, usually on the firewall behind wiring, and it's vacuum hose to the intake manifold, if hose cracks it will cause issues like you describe.
But no worries on running without ECT connected, may get a CEL(check engine light) if your '88 has one.