You WILL see varying voltage from the fuel tank sender wire assy...
remember, there is power to the pump, there is also reference for the level sender that will be anywhere based of gas level.
When people change the can fuel filter they have only done half the job. If the can was full of crap, the strainer is just as full. Dirt/rust has to go thru the strainer thru the pumpto get as far as the can. If it went that far there is a fair chance the pump is damaged or worn.
Pull the tank door off, then the tank access plate. Lift sender assy up and out. Be careful not to tweak the float arm or it wil never be accurate again.
Best to change the pump and strainer on the bottom. Siphon all the gas out and see what kind of trash and junk is still in the tank. I reccomend wiping it out as much as possible OR use the siphon tube to suck it out. However you choose, the dirt and crap has gotta go.
Re-assemble and test fuel pressure. needs to be key ON and get to 40 psi and hold that for near an hour and then slowly loose the remaining 35 psi over the next 6-10 hrs.
It sounds to me that there is a LOT more going on than you are describing. New vette owners have the worst time trying to describe what they see/hear from an engine they have no experience with. They don;t know if it is supposed to lope at idle, or if its really supposed to cold start idle up to 1100 rpm then go down to 600 by itself. They don;t know. Thats why we are here.
Before going further you will need these basic tools:
Fuel pressure gauge
Noid lites
DVM (volts, amp, ohms)
small dentist mirror on telescopic stem
Techs Stetiscope
spark tester
sm wire brush set
silicone ign grease
GM edition FSM with color electrical drawings
Follow the FSM flow charts for diagnostics. They are never off course.
Use only Delco ignition parts (electronic ign HEI, ESC etc)
Go back and set all sensors, tps, ck IAc for function and ck for vac leaks everywhere.
Once you've proven the basics to be ok, then you can start to look for the more exotic failures. Your wire harness is sh*t and probably part of the problem. Look for the harness tape unwraveling and coming apart. Thats where you find splices that are also coming apart....'
Read the FSM and familiarize yourself with the engines operating systems. What they are and how they operate. So when someone here says..." get a good thick layer of silicone ign grease under the ICM and be certain that none of the wires are being pinched..." You will know exactly what they are talking about,.
Try this stuff, note the results and get back to us. It will get there but it will take MUCH longer if you do not follow the FSM
guideline for diagnosing eng performance problems.
Above all, DO NOT attempt to apply 1979-80s mechanics to these cars. They do not do well when "bubba'd" and will usually end up so screwed up that some never get straightened out enough to become a DD. If Bubba approaches your car, CALL 911 and wait for help to arrive !
The Corvette is more complicated than a redneck with a beer in his hand.
Hope this helps in someway....My best advice...get and use that FSM..don;t waste any money on a haynes book or the other books from the parts store. Those are worthless. Junk.
Buy the real GM 2 book service manual and then you can repair the computer even if you're blind.
