OK I watched it and have to say, yours is more interesting then paint drying!

There's similar issues with 98 Chevy trucks where the needle shakes after years, guys have replaced the gauge and sure enough still shakes after a few years. Seems GM packed the stepper motor with grease when they changed to a PWM signal, works well for a few years. The earlier 97 trucks did not have the issue because of old style fuel level and 99 was different body style, so they just patched up this issue on this year truck. As the grease is pushed away or? Well the needle shakes. Mine does but I don't look at it that much.

Here's a thread, 18 pages, where some guys really looked into this and a fix and found one with electronics (capacitors or?)
http://www.pacificp.com/forum/viewto...er=asc&start=0

With that and yours you could go into gas gauge repair, or more accuaratly Instument Panel Repair and Rebuilding. As vehicles get older things like instrument panel repair/rebuild, light bulbs, steeper motor etc... seem to make a good business. Man some of the old muscle cars get big bucks to restore an IP.