Grounding the pink sending unit wire with the key on should move the gauge. If it doesn't, gauge issue. If it does, sender issue.
Of course, the problems could be compounded, I had both a bad fuel gauge AND sender, which made diagnosis interesting. Bad readings from sender, bouncy gauge because the gauge was bad.
I agree with Rene, if it doesn't move at all, it's probably not a sender issue.
After my recent fun with rewiring my gauge setup for the later electric speedo, I can tell you the printed circuit that "drives" the lights and all the gauges is very simple. All gauges essentially have one wire that comes from a sender or switch (headlight dimmer for lighting, oil, fuel) that is on the printed circuit board, all the other "circuits" on the board are simply + or -. '90-91 PCB's are pretty cool, the + and - is actually embossed in the copper, and all gauges/lights share the same +. If one connection goes bad, all will lose power or ground, or you will simply lose the individual input for whichever gauge. I'm having to learn WAY too much about how these things work from this swap.

At least I hope that gives a bit of understanding of how the gauge cluster works. It's not a big mystery. The fuel gauge for instance only has one specific wire for it...in my case it's the same pink one that comes off the tank.
Only problem is that you've got to remove the cluster to get at the PCB, but no problem in my case, I knew there was a reason I haven't yet installed the dashpad.