Check engine - no codes or cannot connect

Yep, it is a fake. (not totally it was in the new design and does allow connection with a scan tool with the correct software, but most will not have that)
Open the hood and look on the drivers side fender and you should find the EEC-IV test connection. You can use the "light flash" method or connect the proper OBDI scan tool to get more data.

https://www.2carpros.com/articles/ford-lincoln-mercury-obd1-1995-and-earlier-diagnostic-trouble-code-definition-and-retrieval

OOF... That's a few codes BUT only 3 really matter and of them one is likely causing another code.

Codes 332 and 558 are related. 558 is the EGR vacuum control solenoid. Either the wiring or the solenoid itself. If it doesn't operate properly the EGR doesn't work and you get the 332 code because the EGR isn't being properly controlled by the PCM. Check the wiring to it and you could test it's resistance as well if you have a Volt Ohm Meter. Damaged wiring or corrosion cause more codes than bad parts.
https://www.2carpros.com/articles/how-to-use-a-voltmeter
Resistance in the EVM coil 20-70 ohms

Code 116 points at the engine coolant temp. or intake air temp. being out of self test range. That could be for several reasons, bad sensor, loose connection or that the temperature during the test was under 50 degrees.
For both the test involves checking the wiring and connections and using a meter to back probe the connection and see what voltage each sensor is actually sending.

One or both are why the CEL light is on as both will call for it. Both can easily be diagnosed with a decent VOM and a couple sewing needles.
This video shows how you can test the wires with the sensor/connector still in place.
https://www.youtube.com/watch?v=yuzVBd9Hk7k

536, 538 and 632 are simply because you probably only pulled the codes themselves. Ford has a complete cycle you do with the factory scan tool where you plug it in, then get KOEO codes, then start the engine and look at KOER codes and do things like step on the brake, the gas, shift through the gears, and some others. If you didn't follow those procedures you get those codes.

Easy way to know those three don't matter,
536 - do the brake lights work? yes> code doesn't matter as that is what it tests for, brake switch on/off during the test. If you don't press it OR you hold it on it sets the code.

538 - If you step on the throttle does the engine rev up? Yes> code doesn't matter basically for the same reason as above, no throttle blip during the KOER test.

632 - Does the transmission change gears and the back up lights work? Yes> guess what.....