Wont start my 92 buick skylark intermittently wnot start. I tried the test where you pull the connector of of a injector and check for voltage at the connector and my light lights on both the wires with the ignition on

Make sure battery has a full charge. Have a helper crank it while check for spark at the plugs. If spark everywhere, use a gage and check proper fuel pressure and fuel injector pulse. when testing, let the starter cool off a bit.
I don't know what testing you have done?

Are the fuel injectors squirting fuel ? Does the engine have compression ? How many miles on the vehicle ? Timing chain an gears , these are know to wear an jump time . Do a compression test .

Hey Dan , do you have a volt meter ? Pull head lamp bulb , with lights on check for battery voltage on tan wire left headlamp an lite green right side headlamp ! If there is no voltage back track to headlamp switch , which means pulling the plastic cover from around the upper steering column ! check for battery voltage at the Orange wire in connector # 1 , that is voltage supply to the headlamp switch ! Power going in an no power coming out with the switch in the headlamps on position means your switch is bad !

Did you check for spark at a spark plug ? If there is spark , spray carburetor cleaner in the intake an see if it try's to start , if it try's to start you probably need a fuel pump ! If no spark you have a bad crankshaft position sensor or ignition control module is bad.

You have 2 issues here #1 the engine is running hot . Test the cooling system fans they seem to be not working. #2 car dies i would start with testing the secondary ignition (spark).

do you have power and ground to the injector?do you have spark? a bad ignition module?

You need to run a system fault code test, do that by following the instructions HERE, code are also listed at the site.

You have 35 psi of fuel pressure and injection pulse?

i would pull a spark plug and see if its wet(fuel) sounds flooded but that is the effect not the cause . need to check fuel pressure to find the cause of the problem.

i check to make sur ur fuel pump is working if you can hear running the i would try chevron techron injector cleaner and make sure ur spark plugs n wires r good