2005 saturn ion that seems to be running fine...The engine symbol light is on? What can cause this?

Did you replace the bulb in the passenger side running light/turn signal socket? There are two filaments in that bulb, one for the running light (which you indicate works) and one for the turn signal. If that bulb (filament) is burned out, it will make the turn signal flash faster. I don't know why you were swapping headlights, don't know where the fire box under the hood is, and don't know what a jumper sore is, so can't help you any further. I have a Saturn Ion, and have never found a fire box or jumper sore in it.

a failed engine coolant temperature sensor is the most likely and seems to be a reported issue

https://www.google.com/search?safe=off&rlz=1C1QJDB_enCA643CA644&sxsrf=ALeKk02kSn-QncvywOk9bMNBz7RKSNvZHA%3A1613798578800&ei=spwwYL6oMJaqtQb9g5Q4&q=2006+saturn+ion+2.2l+coolant+temperature

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You most likely have a cylinder mis-fire. Usually a bad spark plug or ignition coil/ignition wire. Check the codes to determine what cylinder is causing the misfire and repair a necessary

When the light is on have it checked for DTC'S - diagnostic trouble codes , do you know what they are ? Ignition system problem , coil's , plug wires if the vehicle has then . The check engine light code is probably for a engine misfire . Check Engine Light On

The coolant light is a bad thing. You need to check the coolant to see if it is low. That would cause the light to come on. IF it is low you could over heat the engine and that would cause a major problem.

I would begin with the fuel pump relay and see if it is being powered after the engine starts.

That sounds like battery--wiring-or starter. Check the battery voltage. It should be 12.6. volts with engine off. Clean the battery terminals.

if this is a GM product with a 16v engine of 2.00 litres then its the same as a astra or a vectra along with the zafiro all europeon named models or a holden in aussie and as such although i have never seen one it could have a common engine with a different car body shape and as such common faults on these engines from around this year and earlier they suffer from this problem and as such what i do here is to fit a earlier crank sensor that fits to the front pulley of the engine and disconnect the crank sensor in the block ,watch polarity on the two wires as one way it will be the same and the other way around they work ok i think the problem is a build up of residule magnatism in the crankshaft causing the computer to play up .If you vehicle isnt fitted with the toothed front pulley or the suppot bracket then take one off a earlier engine in the scrapyard

ck your drive belt. and fluid levels

I am not a mechanic and have had no problems with my 2005 Ion-2 but at msn/autos I see that these can exhibit a starting problem because of the ignition switch which they recommend replacing. The part is around $40 & the labor is 1 hr.