First-gen Vees normally run two bars, three if things are getting extra-steamy. The fan should kick in before you see four. For reasons unknown, Wees get one more bar.
Anyhoo, yep, you should be able to unplug the temperature switch and jumper the terminals inside the connector to get the fan to come on.
One thing that can happen (or at least it happened to me) is that the plastic shroud around the fan can shift or warp and keep the fan blades from turning. So with the bike off, reach in there with a finger and make sure the fan can turn freely.
And of course check the fan fuse. If the fan couldn't turn, it could pop the fuse.
I've also seen bad temperature switches on other bikes. There's a spec in the shop manual for the temperature at which the switch should close.
2002 Suzuki DL1000 V-Strom, Dark Metallic Space Blue
1983 Suzuki GS850G, Cosmic Blue
2005 KLR685, Aztec Red - Turd II.2, the ReReTurdening