OK lets take it from the top.
Why are you pulling the engine apart ?
What you have there is a Powertorque Mk I with an LM carburettor.
The coil is controlled by that small silver box with the brown wires at one end and the black wire at the other.
Usually the rivet holding it on becomes loose and can not maintain a good earth. So you get an intermittant ignition.
The on off is where the wires go into the carb
The rest here are general instructions.
To remove the switch set the throttle control fully open.
pull the black earth cut out wire out of the rubber boot If you spin the engine at this stage you should get a spark.
If the control module is loose slip apadle pop stick under the end with the brown wires to keep a good earth at the other end.
Now pull the boot and brown wire strait out together.
The boot and the rubber tip you should find on the end of the brown wire are service items and should be replaced every 10 years and your engine could be 40 years old.
There should be a serial number and year stamp in the block under the carb, The year may be full 4 digits or shortened 2 digit.
The boot goes over the wire before the tip is replaced or you bugger the boot.
When you turn the engine off a peg in the carb hits the rubber tip on the brown wire & pushes it foreward so it contacts the black wire and shorts out the coil.
The only thing that opens the connection again is the springyness of the rubber boot which degrades over time.
The entire carb is on a boynoet type fitting so you push it in against the spring washer, rotate it 1/4 turn & it will pull strait off.
The two PVC tubes should also be replaced.
The upper one in the photo is the govenor and it slips easily off the carb end.
To test the diaphragm, blow & suck through the tube you should hear & feel the diaphragm move in and out but it must be airtight, if you can blow or suck continously then the diaphragm needs replacing.
Under the carb the second tube goes to the decompressor which sits on a plastic damper in the carb, be careful pullin it off as the white damper tube is easily broken and is NOT REPLACEABLE so the carb body is then trash.
Same test here blow & suck to activate & deactivate the decompressor diaphragm and again only a small amount of puff, continious a flow then decompressor need repairing or replacing ( late ones are not servicable )
To remove the throttle cable, set it to the stop position, loosen the clamp on the snorkel tube and pull the tube back exposing the throttle cable.
If you are right handed hold the carb in your left hand with the throttle cable at the 3'0 clock position.
Grasp the throttle cable in your right hand then twist it to the right.
The ball will pop out of the cam and the the outer cable is pulled directly back towards yourself
Now wash the carb body thoroughly before attempting to remove the diaphragm cover.
If the engine was responding to load properly and it tested OK when you blew & sucked through the tube, then do not remove the cover as once opened the diaphragm will need to be replaced.
The diaphram cover and spring cap are removed together and will pop off by inserting a screwdriver in the join and twisting . You should see a few pry points.
When it does there is a long spring that will fly out
The retaining plate now exposed has a keyhole retainer remove it.
The diaphragm simply pulls off the barb on the end of the poppet valve, but it is a very tight fit as it has to be airtight for the diaphragm to work
There is a shorter spring under the diaphragm, then a lift guide ( spider ) , then the throttle cam & optional brass compensating shims ( up to 4 of them ) .
The valve comes out from the other side & is the only thing that goes in from that side.
The primer cap can be removed, the screw in the middle is the main jet.
The float and needle will generally fall off and the needle is tiny so do it over a bowl.
Generally there is nothing that needs servicing inside the float chamber they never ever give any problems unless the primer bulb need replacing.
Once removed the O ring on the primer plate will need to be replaced and when you replace the primer plate, push it in around the edge then tighten the main jet , just snug or you will break it or the plastic tube it goes into.
The most common reson for replacing an LM carb is a gorilla on the end of a screwdriver ripping out the main jet tube.
The manifold on the engine should also be removed ( 2 screws) it has 2 O rings on it and both should be replaced ( 10 year sevice items )