96 Saturn wagon. temp light flashing. not overheating and just replaced water pump. any thoughts?

Hi there:
In some vehicles, when water coolant level sensor go to bad, the warning come on in dashboard.

I suggest check this level sensor and replace it.

not a water pump , ,just a lack of coolant and air locks
have the engine compression tested to check for gasket or cracked heads

plenty of water in the reservoir
none in the radiator
the coolant level sensor is in the radiator and if it is flashing , that indicates no water in the radiator tank and that is the cause of the overheating

local libraries sometimes have haynes manuals.that will tell you where it is.could be oil pump too,but does sound like thermostat.

how about the coolant temp sensor, they had alot of problems with that sensor and also the plug for it,some have two of these sensors side by side, one for the gauge and the other for the fan, i would replace these first and go from ther good luck,

Wow, that's a tough one, if you've done all that and it still overheats, I would try replacing the temp sensor, maybe it's faulty. Plus they're pretty cheap( I like fixing things for cheap)
If that's not the problem you could try a lower temperature thermostat, and if that doesn't work I would suspect that something is preventing the coolant from moving through the block effeciently.
Where is the temp sensor?
I had a Buick that the temp sensor was on the top of the block and if the coolant level went down AT ALL it wouldn't cool the sensor and it registered as dangerously hot and give me a heart attack in the process.
As for a tune-up get anew distributor cap, rotor, spark plugs( and spark plug wires if you want it to REALLY be tuned up)
This will probably cost you in the range of 50-100
bucks, but a little preventive medicine goes a long ways.
I had a bad plug wire I thought was an ignition problem and spent 300$ in parts trying to fix.
One day I went "I wonder if it's the plug wire?"
I bought one for 8.88$ and now it runs like a brand new car.
Hopefully one of these things will work.

you've got a possible blockage in the head or block.

If the temp gauge is reading normal, the lights are flashing, and the coolant level is full, the level sensor in the coolant bottle is the problem. I'm a service consultant for a Saturn dealer and I've run across this many times.

My instrument panel is doing the exact same thing. It started today. I almost think it may be a loose cable to the computer that drives the lights. Did you ever resolve your issue?

Be sure your coolant level is OK first. When a water pump or other cooling system part is replaced air blocks in the system are not uncommon. If the engine overheated, this could have fried the coolant temp. sensor (ECT) causing the hard starting. (It might think the  engines always hot) ECT are pretty cheap. Just replace it and see what happens.