961 poor starting

Is the Choke operating correctly?

Do they even have a choke?. Modern computer controled lean burn engines possibly  use a temperature sensor to richen the mixture for starting, If that fails?.

Petrol engines must have a choke if they have a carburettor but of course, this is computor controlled, but it will have 'enrichment' to start, perhaps the temp sensor is not doing its job?
Having bought several second hand motors in the past, there is very often a 'snag' with the machine-that's why it is sold. Could be best to buy from a dealer, pay the extra premium so 'when/if' it goes wrong you can get it sorted for minium effort/cost!

They are fuel injected not carbed. Contact Stu Bodycote

Would the bike be new enough to have an OBDII port ? A 2002 Triumph I played with had one and the error codes could tell you about iffy sensors , relays and fuel pumps that were contributing to the Engine Management Light coming on.

Difficult starting is pretty standard as the SE has massive injectors (the green bosch injectors on the SE are much bigger than the later bikes smpe bosch copies) and no idle air control. Once you've eventually got it to catch, and warmed up, it should be fine. Because of the injector size, they can also flood easily.
Yes primary side can sound like a cement mixer with a few bricks bouncing around.
Flickering warning lamps is down to electrical noise...normally exaggerated by turning the headlamp on. There's a technical service bulletin for each lamp and requires resistor leads placing in each circuit to suppress the noise/interference.
Cheers for the shout outs guys!

My second 961 developed engine starting problems on its 3rd day of ownership.
NML thought that it was the ignition timing sensor and sent me a replacement. This fits at the front of the engine over the camshaft.

That did not work, so the bike was collected for a factory check-up. The problem was eventually tracked down as a blocked breather pipe.

The bike was returned to me with a flat battery.  Wonderful!!! 

Highly recommend having Stu Bodycote do a full health check on the 961. Sent my 2012 Mk 1 Sport to him after experiencing a gear selection problem which turned out to be a simple fix (clutch basket securing nut had loosened) but whilst with him got the thorough health check done. Fixed a number of small niggles I'd just ignored , like warning light anomalies (fitted electrical patches) and a weeping head gasket (retorqued head) but also did a number of recommended jobs , like fitting his breather mod , securing the gearbox sprocket nut properly with the tab washer (not done well at the factory) and replacing the copy Bosch components with original Bosch items. Also had a new rear tyre fitted while it was there.

Like a new bike when I got it back after just a two week turnaround. Nobody knows the 961 like Stu. Well worth the reasonable cost.

On starting from cold , don't touch the throttle when pressing the button. Mine fires up immediately , give it about fifteen - twenty seconds of tickover then throttle can be blipped without fear of stalling.

... and another recommended job I had done by Stu when rear wheel was off for a new tyre is replacing all cush-drive rubbers with a more durable one he offers as the originals were a softer compound and become mangled - which mine were.