How to test the Fuel/Gas tank level gauge or the sender?    

As always for ever and ever check fuses first "Meter" fuse.
The sender is JUST a variable resistor, in fact , some guys, rewind it with new nichrome wire.
Technically it's a Rheostat ( 2 wires)
The tests are easy and simple.
Best practice is to assume the easiest to replace parts are bad, not the tank drop idea.
  • Bad wires?  (no 12vd to rear bumper  conn, yell-read, key on? unplugged)
  • Bad connectors (corrosion, big time)?  if this happens the gauge will read low or Empty.
  • Bad Guage? (rare but we always check , just in CASE) Fate does rule earth, not statistics.
  • Bad sender last. (but is very easy to test on car, no need to guess)? Use the OHMS resistance scale Rx200.
This order above saves labor. And time.  (Draining the tank , is not fun)

Check the guage first.
Then pull the connector at the rare bumper or left tail light and test the guage from there.
Then test the sender from the rear bumper connector.  (ground the wire or use a lamp to ground see guage go to full)
If meter is good, then the tank sender is bad.  (or wires)
If this fails, check voltage at the yell-red wire , unplugged, if not 12vdc key on the path forward is bad.
If the meter (gauge in dash) is dead, then you don't now how much fuel is in  the tank, so fill it. now.
The tanks is now full, and the sender will read about 3 ohms, full. Even 1 ohm good.  (infinity is bad)
Measure the sender ohms 2 ways,  across the 2 wire, then each wire to the body. 
Keep in mind the body grounds love to fail on Suzuki, all external grounds.
If you read open on the 2 pins, of the sender (or at rear bumper) the sender is bad or the unseen connector on top is bad.
If that passes, and the hot wire (yell-red), to ground is open, then the body ground is bad.
The sender, reads 1 to 5 ohms with a full tank.

SUZUKI P/N: #34810-60A11

This Suzuki Sensor fits 1989 to 1995 Sidekicks, Trackers, Vitara's ,Sunrunners and some Santana's(Spain Kicks) but not any Samurai.
The connector on the end (above) loves to go bad.

1.6L Sidekicks, non Sport 1.8L.

To test this , DMM  or analog multimeter tool  $12 DMM sold, will work here,  even one at WALMART.

See my  pump test page here.

Generation 1:
For the light bulb use any GE#194 Sidemarker (runGning lights) bulb. (perfect 0.27 current)

Test is almost like testing the Coolant Guage.

Note, this is an acid test. afterwhich there is no guessing.  why guess?

On newer cars the Yellow-red wire is yellow black.
The Sender is a black wire that goes to body ground which in most cases will be bad. 
Check the grounds, make them perfect.

This is the factory page,  the tests are very simple.
Most tech.'s  use a #194 car side lamp to test the gauge (step3),  this works best, because it prevents the guage from overheating
The gauge is not really a true voltmeter (magnetic) it is thermal device.
But it is true  if you do the test fast, with no lamp there will no damage to the gauge.  (the early books show just that)
Fast means, less than 1 minute. IMO.

Starting in March 1996 (see page) The Sender was upgraded to from %3 accuracy to about 1% to allow the new EVAP2 OBD2 spec. to work correctly (Fed. EPA rules) The tank must have air space on top now, to do the EVAP2 tests, the old sender don't cut the mustard. And all new part numbers.   (connectors are same but new colors) The TSB I think has an error, it should say this.
"the sensors are interchangable, but you must not use a EVAP1 sender in any EVAP 2 car (built after March 1996)
EVAP 2 is easy to see, (GM glove box RPO codes) or the presence  of the new top of tank  pressure sensor , part ID 12 here.
In truth the  new pressure sensor does not work right with a full tank off fuel , thus, all this fuss.
But the tests on this sensor remains the SAME.  1 ohm full,  127 ohms empty (extreme spec)
I mention these facts, so you don't later fail the EVAP 2 tests. (a great horror that....)

A TSB on subject of EVAP level 2 senders.

TSB = factory Trouble(or Technical) Service Bulletin
This TSB is for fine tuning the accuracy but shows clearly the readings !!!

This sender is inside your tank:  from the top surface (of course) down.

part 38 below

Tank Harness: < click
see ground G402 behind Left Rear tail light, if bad ground ,pump and maybe gauge will be bad.

See on top of tank , a real photo

Generation 2  (1996 example)  Please deactivate AIR BAG FIRST ( they are lethal to mechanics) when messing with the DASH  GAUGE.
Tanks / Gauge tests see page 9 and 10.
Page 9:

Page 10:

In later generations (3) this fuel  meter is  driven from the ECU/PCM directly and is modified voltmeter D'Arsenval type.
The Grand Vitara (not Vitara) and XL7  went to ECU direct meters in 2003.
Quite  unlike the above Gen1/2, thermal heating meters.  Do treat them differently during all tests.

The tank sender can vary from 1 Ohm(full) to 128  Ohms (empty) up to 1998 year. ( and beyond)

THE TANK:   (early) no EVAP 2 parts. yet.

In March 1995 (build year, not model year,) they added a EVAP2 pressure sensor to the top of the tank.

Photo by: Cosmic_Splatter. Thanks.

rev: 4  1-4-10 (added generations data)  revised 8-20-2014 for all part numbers and why they vary.  and testing order.