GM Minivan Inaccurate Fuel Gauge

I've bought a 2001 GM Oldsmobile Silhouette Premiere minivan. The mileage
is relatively high (82,000), however my closest examination (and I've does
as much as overhauled engines and such in the past) indicates that it was
very well cared for.

The only issue I find with it is that the fuel gauge tends to wander all
over the place while the vehicle is parked. After I get it on the road and
up to speed, it settles down. But while idling it may raise high or drop
low. When it falls low, the engine data light comes on showing "low fuel."
Sometimes the engine data light shows "low oil" instead.

This does not seem to be directly connected to engine speed--revving the
engine while in parked doesn't change it. It only becomes steady and
accurate while I'm actually driving.

I saw a title to one service bulletin for the 2004 model concerning
inaccurate fuel gauge problems, but I can't see from the title if this is
the same problem.

Is anyone familiar with this issue?

Just a thought....instrumentation voltage regulators have been used to
supply a very stable
voltage source to the gauges in some cars. There have been cases where those
things lose
control and the voltage stability suffers.

Typical other issues involve bad ground connections, corrosion in
connectors, etc.

I may be way off, but this is where I would start looking.