That New Old Bike Is Turning Me Crazy (daytona 955 Inside)

Hello to all the Triumph lovers
After twenty years without motorcycle, I just bought a Daytona 955i from 2003 with 3000 km !
It didn't move for the last ten years, and so....But it was stored in a warm and dry place, so no issue with bad electrical connections....(well I'm hoping so)
Bike looks like new, show room condition all original...(silver)
BUT.......
We tried to start it, after draining water, gas and oil, (water was looking like Coca cola, same color!) and here is the moment.....key, start .... And Nope, zero, nothing....
New battery, fuse of the starter melted, we open the gas tank, has pump and all the linkages inside completely rusted and rotten. Pump didn't do anything, dead....
We change the pump, all the rubber linkages and the filter inside the tank, and miracle! the engine starts....YES ! stable around 1200 rpm, respond, seems like there is no problem anymore...Drove 100 meters no problem, respond to the throttle, all good....
BUT....
Stopped the engine and no way in hell to get it running again....
(Hey it's a Triumph)
I leaved the bike 24 hours alone, and then tried to start it again....And....It works!
Engine is running around 1200 rpm, then starts slowing down and stops completely after 2/3 minutes....
Tried to start it again, starter is running, but zero explosions, nothing......
Does someone have an idea of what could ne that issue?...
I ordered the ECU cable...But in the meantime maybe if there a simple cure for that problem or of someone did have that kind of issue...remember bike is almost new....
Thanks for reading...HELP !
By the way, just to make sure, the drain with the red plug goes to the pump or is it the white one? I don't remember...Red is going left on the engine injection , white on the right...

 

Thanks yes, sounds like a lack of fuel for a mysterious reason....
I'm so tired to search, I bring it to a Triumph dealer on saturday....

 

Thanks for all the advices. A Triumph dealer picked it up this afternoon, I'm tired of searching...
Where are the good times with simple carburators and simple non electronic ignition....i would have find out already for a long time...
I wanted the bike serviced anyway, so...
We'll see what the mecanics will find...

 

Seems like it doesn't matter...Some do have the red on top like mine, other the white one...The system works both ways...

 

Ok We think to have found the problem
Inside the tank are several short pipes going from the pump to the filter, and it seems like those houses are rotten and part of the pressure of the pump is wasted in the tank....
The dealer tried to run the bike with the tank of another bike and it works, so......

 

Thank you ..
We find the problem....Inside the tank are some rubber pipes going from the pump to the filter and from the filter to those damned plastic nipples...You know what I mean....And these rubber pipes were rotten. Looked good but porous and the pump 3.5 bar became....Zero...
We change them and all is good now....
I'm a happy rider.....