The noodle is present and attached to the control cable inner and outer as clearly shown in the colour picture that you uploaded
I will attempt to help you ID otherwise you will waste money obtaining the correct part .
Follow the black outer gear cable that runs from the handlebar zone and along the cruciform then onwards past the crank arm and pedal
ADVICE or ( Safety warning ) should you be tempted to test ride without the reccomended pedals you may snag your heal on the ill fitting cable
Back to the plot .....you will discover a small aluminium/chrome tube which currently disapears into the lower boom tube .
That is in fact the NOODLE referred to
Its exactly the same as the pair of curved noodle tubes attached as guides to your SA brake system .
Previous owners and hidden life ???
If a bike is offered cheap and the vendor only accepts cash or wants to sell OFF
ebay .
Alarms bells should ring
Was it supplied by a friend call David Nosurname at the local pub
Sometimes its a false alarm and by asking a few simple questions you can grab a real bargain
The good news very few recumbents have been stolen (if nicked you would get a report by eagle eyed forum members )
I suspect your machine popped up on Gumtree last year
The vendor stated ,when questioned, that it started life at a special needs school in London
So at that point it probably had 60 previous owners
It was removed from service needing a major sort out and sold to a staff member
Who quickly sold it on to a teaching pal based in London
The trike was relocated and stored in Lincolnshire ??? due to lack of space in a shared flat
Eventually sold ........last year to who knows but you can probably guess
If the above is accurate info
It explains why your Adventure has such a basic spec which is very rare
and picked up unexpected wear and tear to the seat cover and other elements of the trike
The serial number could be used to confirm the first owner and validate the above info or story
Hope that helps and by the weekend your out riding in a safe manner .