I just ran into this issue with my mother-in-law's '99 GMC truck, and posted something in another thread.
Before you start throwing money at parts (which can get very expensive), I'd run a tank or two of the recommended dosage of Techron Plus additive. My MIL's gauge would constantly bounce up and down, fuel light blinking on/off, no matter how much gas was in the tank. The Techron Plus advertises that this erratic behavior can be caused by deposits (I think sulfur) from sub-par gas on the fuel sending unit contacts. Chevron claims the Techron Plus can remove these deposits, restoring proper functioning. At $7/bottle, I tried two in my M-I-L's truck (her 25 gal tank required two bottles, you may get by with one). Within 100 miles, her gauge suddenly began reading correctly, without the erratic jumping. I can't guarantee it will work on yours, but it saved my M-I-L $274 for the new fuel pump/FSU assembly. And the Techron was on special at Advance Auto 2 for one. So, a $7 fix.
There may be other gas additives that can do the same type of cleaning of the contacts on the FSU. But the Techron was available, and the Plus even has the claim right on the bottle. I don't know about the previous version of Techron removing these deposits, or if/how the "Plus" is different. But it would definitely be worth a shot, plus the added benefit of a fuel system cleaning.
In answer to your question about a ground causing it, that is a possibility. It would be more of a concern if you lived up north with salted roads. I don't know how your Camaro's ground system works, but I would think a bad ground for the FSU would also cause issues with other parts, as grounds are often shared.
Here's what I would do in your situation:
1) Run a tank or two with recommended dosage of Techron Plus
2) Pull codes from your ECU (being a '98, it is OBDII compliant). Even with no "Check Engine Light" on, there may be stored codes for a problem. I don't know how easy the Camaro is to pull codes, but my '97 Maxima only requires a screwdriver and watching for blinks. Easy and free. Also pretty thorough throughout the car's various systems. If yours is hard to access/get codes from, move it to number 3.
3) Visually check all of your ground connections, especially any near the tank/backend. Also around your fuse and relay boxes under the hood. But if one of those is bad, I'd guess you'd have other issues.
4) Test your fuel pump/FSU if testable. But this would probably require dropping the tank, which on your car would be a labor intensive job (you need to remove the rear axle I believe).
Here's info from Chevron's site on the FSU issue and Techron:
New 'clean' gasolines can cause fuel gauge malfunction
The Problem:
Certain residual sulfur species found at very low levels in many of todays highly refined gasolines can form corrosive deposits on reactive silver-based fuel sending unit (FSU) components used in many makes of automobiles. The FSU, located inside the fuel tank, reads the fuel level and electronically sends a signal to the fuel gauge.
How sulfur corrosion can cause your vehicle's fuel gauge to malfunction (false reading).
This corrosive deposit can disrupt the electrical performance of the FSU and lead to either erratic operation or complete failure of the FSU, often resulting in artificially low or high (empty or full) fuel level readings on the fuel gauge seen by the driver. An erroneous high (or full) fuel gauge reading could lead to the motorist inadvertently running out of fuel and create a potentially dangerous situation.
The problem is best viewed in medical terms: acute and chronic in nature
Acute: problems occur when the occasional batch of off-specification, high sulfur refinery gasoline leads to extensive erratic FSU operation across a region. The problem can occur in a single tank of gas.
Examples: Louisiana, Florida, Memorial Day, 2004; Erie, PA, Louisville, KY, Canada
Chronic: problems occur after long-term exposure to low-grade sulfur contamination in a fuel, which frequently leads to premature erratic behavior of the FSU at some point.
Examples: New Mexico and Arizona, 2004 and 2005
Higher temperatures play a vital roll in how severely an FSU is damaged by a harmful sulfur-containing gasoline.
FSU failures typically require the complete replacement of the sending unit at considerable expense to either the vehicle manufacturer or the vehicle owner. This repair can cost from $400 to over $1000.
There is strong automaker awareness, as virtually all automakers have been impacted: recalls, warranty repairs, safety concerns and product reputation. Some automakers are beginning to phase out reactive silver-based FSU components at significant expense. However, reactive silver-based FSU components have been used since the late 80's, so a 15 year-plus vehicle population is still exposed.
The Solution:
TECHRON® Concentrate Plus is one of the most advanced fuel system cleaning technologies available in today's market, and many automakers prescribe it routinely as their solution to all fuel deposit-related driveability problems.
One treatment with TECHRON® Concentrate Plus can help:
Clean corrosive sulfur deposits from fuel gauge sensors
Restore operation of sulfur contaminated fuel gauge sensors
Prevent harmful sulfur species from attacking sensitive electronic fuel sending units
Protect the FSU against malfunction by coating all metal surfaces of the fuel system
Hope this helps.
Dave
