How do i wire a after market tacometer to a 04 883 sportser it has 4 wires, lamp, ignition coil,and earth (thats the ezy 1 )

I think it's a magneto ignition which means it should spark unless the (white ?) wire between the coil and the ignition module is earthed. To stop the motor this wire is connected to earth by either the key switch (turning key to "Off") or the ignition relay drops out (can happen if the seat switch is not switched on). Probably worth checking the seat switch is working reliably early on.
Simplest way to check is to find the stop wire and disconnect it (leaving the coil connected to the ignition module). You'll have to re-connect to stop the motor, or short the coil - ignition module wire to earth.
See bottom circuit diagram.
Good luck.

check the wiring connections inside ignitor plugs and follow wiring harness from ignitors along the wiring harness as it sounds like ther is a break in the earth wire that feeds 1 and 4 cylinders open the insulation along from the harness where it bends to see if ther is not a bad connection where a wire from both 1 and 4 connect together in the harnes normallly within 30cm of the ignitors inside wiring harness

Hi , there will be 3/4 wires at the fuel tank gauge. 1 ground wire ,1 gauge(on dash) wire, 1 gauge low level indicator light (warning on dash) Get a test lamp , ground test lamp and probe each wire. 1 will do nothing (earth wire) 1 will bring on dash low fuel light , the other will be the gauge on the dash which will rise (slowly) to the full position.

Is there a security system on the bike? If not, might have shorted wires to ignition, or a weak coil. Charge battery to full charge, the put load tester on and ensure there are no dead cells.

Remove the plugs from the head. Insert into the coil wires. Make sure they are properly earthed on the engine. Crank the motor and check for spark at each of the plugs.
Refer to the diagram. Cylinders are connected as shown on the diagram in blue. 1 goes to cylinder 1(sparkplug furthest from coil pack), 2 to 2, 3 to 3 and 4 to 4(closets to coil pack).
To test the coil pack use a digital volt meter. Measure resistance between coil towers for coil 1(marked 1 in red on diagram) Value should be between 12000 and 14500 ohm. Do the same for coil towers 2.
Measure resistance between I and C1. If the measurement is more than 5 ohm the coil is defective. Do the same for I to C2.
Measuring voltage at I(Ignition start/run) to ground should be 10V.
I is connected to the 15A engine fuse. The radio interference capacitor is connected between this line and earth at the coil. Disconnect it to see if it cures the problem.
C1 and C2 connect to the powertrain control module.
Bear in mind that aftermarket coil wires may cause problems with misfiring, so see if you cant find an OEM coil wire to replace the broken one before replacing anything else.

Hi ebrown80
You can splice into each wire in turn at the back of the lamps.No need to cut right through the origional loom completly. For a really good joint you should spot solder each connection and insulate all joints well. Tow bar sockets operate on a common earth, so no need to loop each one.
Check back of socket and you will find each pin has a number. 1---7
The wiring colours from the socket back to the loom are as follows
No 1 Pin--- Yellow Wire---Left Side Flasher
No 2 Pin--- Blue Wire------Fog Lamp.
No 3 Pin--- White Wire--- Earth. Must have good contact or nothing else will operate.
No 4 Pin----Green Wire--- Right Side Flasher.
No 5 Pin----Brown Wire---- Left Side Park Light
No 6 Pin----Red Wire-------Brake Lights
No 7 Pin----Black Wire----Right Side Park Light. Centre Pin.
I hope this helps you out
Best of Luck with it
John

black socket, black 7 core wire
pin 1 yellow left indicator
pin 2 blue, rear fog light
pin 3 white earth
pin 4 green right indicator
pin 5 brown right side/tail light
pin 6 red brake lights
pin 7 black left side/tail light

Grey socket grey 7 core wiring
pin 1 yellow, reverse
pin 2 blue, supplementary feed (ignition)
pin 3 white, earth
pin 4 green live feed (battery +)
pin 5 brown not connected
pin 6 red supplementary feed (ignition)
Pin 7 black earth

On the discovery there is a purpose made plug behind the panel on the drivers side rear, behind the rear lamp
i think the relay you have bought is for lamp failure you just need a normal 4 pin 30 amp relay.
Good luck Davelee